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Introductory Statistics

Barbara Illowsky, Susan Dean

Chapter 13

F Distribution and One-Way ANOVA - all with Video Answers

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Chapter Questions

01:57

Problem 1

Use the following information to answer the next five exercises. There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?

Write one assumption.

Heena Haldankar
Heena Haldankar
Numerade Educator
01:52

Problem 2

Use the following information to answer the next five exercises. There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?

Write another assumption.

Heena Haldankar
Heena Haldankar
Numerade Educator
01:40

Problem 3

Use the following information to answer the next five exercises. There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?

Write a third assumption.

Heena Haldankar
Heena Haldankar
Numerade Educator
01:41

Problem 4

Use the following information to answer the next five exercises. There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?

Write a fourth assumption.

Heena Haldankar
Heena Haldankar
Numerade Educator
01:19

Problem 5

Use the following information to answer the next five exercises. There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?

Write the final assumption.

Heena Haldankar
Heena Haldankar
Numerade Educator
02:27

Problem 6

State the null hypothesis for a one-way ANOVA test if there are four groups.

Heena Haldankar
Heena Haldankar
Numerade Educator
02:31

Problem 7

State the alternative hypothesis for a one-way ANOVA test if there are three groups

Heena Haldankar
Heena Haldankar
Numerade Educator
01:14

Problem 8

When do you use an ANOVA test?

Heena Haldankar
Heena Haldankar
Numerade Educator
05:38

Problem 9

Use the following information to answer the next eight exercises. Groups of men from three different areas of the country are to be tested for mean weight. The entries in the table are the weights for the different groups. The one-way ANOVA results are shown in Table 13.13.
$$\begin{array}{|l|l|l|}\hline \text { Group 1 Group } & {2} & {\text { Group } 3} \\ \hline 216 & {202} & {170} \\ \hline 198 & {213} & {165} \\ \hline 240 & {284} & {182} \\ \hline 187 & {228} & {197} \\ \hline 176 & {210} & {201} \\ \hline\end{array}$$

What is the Sum of Squares Factor?

Heena Haldankar
Heena Haldankar
Numerade Educator
04:11

Problem 10

Use the following information to answer the next eight exercises. Groups of men from three different areas of the country are to be tested for mean weight. The entries in the table are the weights for the different groups. The one-way ANOVA results are shown in Table 13.13.
$$\begin{array}{|l|l|l|}\hline \text { Group 1 Group } & {2} & {\text { Group } 3} \\ \hline 216 & {202} & {170} \\ \hline 198 & {213} & {165} \\ \hline 240 & {284} & {182} \\ \hline 187 & {228} & {197} \\ \hline 176 & {210} & {201} \\ \hline\end{array}$$

What is the Sum of Squares Error

Heena Haldankar
Heena Haldankar
Numerade Educator
04:04

Problem 11

Use the following information to answer the next eight exercises. Groups of men from three different areas of the country are to be tested for mean weight. The entries in the table are the weights for the different groups. The one-way ANOVA results are shown in Table 13.13.
$$\begin{array}{|l|l|l|}\hline \text { Group 1 Group } & {2} & {\text { Group } 3} \\ \hline 216 & {202} & {170} \\ \hline 198 & {213} & {165} \\ \hline 240 & {284} & {182} \\ \hline 187 & {228} & {197} \\ \hline 176 & {210} & {201} \\ \hline\end{array}$$

What is the df for the numerator?

Heena Haldankar
Heena Haldankar
Numerade Educator
03:59

Problem 12

Use the following information to answer the next eight exercises. Groups of men from three different areas of the country are to be tested for mean weight. The entries in the table are the weights for the different groups. The one-way ANOVA results are shown in Table 13.13.
$$\begin{array}{|l|l|l|}\hline \text { Group 1 Group } & {2} & {\text { Group } 3} \\ \hline 216 & {202} & {170} \\ \hline 198 & {213} & {165} \\ \hline 240 & {284} & {182} \\ \hline 187 & {228} & {197} \\ \hline 176 & {210} & {201} \\ \hline\end{array}$$

What is the df for the denominator?

Heena Haldankar
Heena Haldankar
Numerade Educator
04:07

Problem 13

Use the following information to answer the next eight exercises. Groups of men from three different areas of the country are to be tested for mean weight. The entries in the table are the weights for the different groups. The one-way ANOVA results are shown in Table 13.13.
$$\begin{array}{|l|l|l|}\hline \text { Group 1 Group } & {2} & {\text { Group } 3} \\ \hline 216 & {202} & {170} \\ \hline 198 & {213} & {165} \\ \hline 240 & {284} & {182} \\ \hline 187 & {228} & {197} \\ \hline 176 & {210} & {201} \\ \hline\end{array}$$

What is the Mean Square Factor?

Heena Haldankar
Heena Haldankar
Numerade Educator
03:58

Problem 14

Use the following information to answer the next eight exercises. Groups of men from three different areas of the country are to be tested for mean weight. The entries in the table are the weights for the different groups. The one-way ANOVA results are shown in Table 13.13.
$$\begin{array}{|l|l|l|}\hline \text { Group 1 Group } & {2} & {\text { Group } 3} \\ \hline 216 & {202} & {170} \\ \hline 198 & {213} & {165} \\ \hline 240 & {284} & {182} \\ \hline 187 & {228} & {197} \\ \hline 176 & {210} & {201} \\ \hline\end{array}$$

What is the Mean Square Factor

Heena Haldankar
Heena Haldankar
Numerade Educator
03:47

Problem 15

Use the following information to answer the next eight exercises. Groups of men from three different areas of the country are to be tested for mean weight. The entries in the table are the weights for the different groups. The one-way ANOVA results are shown in Table 13.13.
$$\begin{array}{|l|l|l|}\hline \text { Group 1 Group } & {2} & {\text { Group } 3} \\ \hline 216 & {202} & {170} \\ \hline 198 & {213} & {165} \\ \hline 240 & {284} & {182} \\ \hline 187 & {228} & {197} \\ \hline 176 & {210} & {201} \\ \hline\end{array}$$

What is the F statistic?

Heena Haldankar
Heena Haldankar
Numerade Educator
04:03

Problem 16

Use the following information to answer the next eight exercises. Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in the table are the goals per game for the different teams. The one-way ANOVA results are shown in Table 13.14.
$$\begin{array}{|l|l|l|}\hline \text { Team } 1 & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} \\ \hline 1 & {2} & {0} & {3} \\ \hline 2 & {3} & {1} & {4} \\ \hline 0 & {2} & {1} & {4} \\ \hline 3 & {4} & {0} & {3} \\ \hline 2 & {4} & {0} & {2} \\ \hline\end{array}$$

What is SS between?

Heena Haldankar
Heena Haldankar
Numerade Educator
04:08

Problem 17

Use the following information to answer the next eight exercises. Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in the table are the goals per game for the different teams. The one-way ANOVA results are shown in Table 13.14.
$$\begin{array}{|l|l|l|}\hline \text { Team } 1 & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} \\ \hline 1 & {2} & {0} & {3} \\ \hline 2 & {3} & {1} & {4} \\ \hline 0 & {2} & {1} & {4} \\ \hline 3 & {4} & {0} & {3} \\ \hline 2 & {4} & {0} & {2} \\ \hline\end{array}$$

What is the df for the numerator?

Heena Haldankar
Heena Haldankar
Numerade Educator
04:18

Problem 18

Use the following information to answer the next eight exercises. Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in the table are the goals per game for the different teams. The one-way ANOVA results are shown in Table 13.14.
$$\begin{array}{|l|l|l|}\hline \text { Team } 1 & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} \\ \hline 1 & {2} & {0} & {3} \\ \hline 2 & {3} & {1} & {4} \\ \hline 0 & {2} & {1} & {4} \\ \hline 3 & {4} & {0} & {3} \\ \hline 2 & {4} & {0} & {2} \\ \hline\end{array}$$

What is MS between?

Heena Haldankar
Heena Haldankar
Numerade Educator
04:00

Problem 19

Use the following information to answer the next eight exercises. Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in the table are the goals per game for the different teams. The one-way ANOVA results are shown in Table 13.14.
$$\begin{array}{|l|l|l|}\hline \text { Team } 1 & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} \\ \hline 1 & {2} & {0} & {3} \\ \hline 2 & {3} & {1} & {4} \\ \hline 0 & {2} & {1} & {4} \\ \hline 3 & {4} & {0} & {3} \\ \hline 2 & {4} & {0} & {2} \\ \hline\end{array}$$

What is SS within?

Heena Haldankar
Heena Haldankar
Numerade Educator
03:38

Problem 20

Use the following information to answer the next eight exercises. Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in the table are the goals per game for the different teams. The one-way ANOVA results are shown in Table 13.14.
$$\begin{array}{|l|l|l|}\hline \text { Team } 1 & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} \\ \hline 1 & {2} & {0} & {3} \\ \hline 2 & {3} & {1} & {4} \\ \hline 0 & {2} & {1} & {4} \\ \hline 3 & {4} & {0} & {3} \\ \hline 2 & {4} & {0} & {2} \\ \hline\end{array}$$

What is the df for the denominator?

Heena Haldankar
Heena Haldankar
Numerade Educator
04:16

Problem 21

Use the following information to answer the next eight exercises. Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in the table are the goals per game for the different teams. The one-way ANOVA results are shown in Table 13.14.
$$\begin{array}{|l|l|l|}\hline \text { Team } 1 & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} \\ \hline 1 & {2} & {0} & {3} \\ \hline 2 & {3} & {1} & {4} \\ \hline 0 & {2} & {1} & {4} \\ \hline 3 & {4} & {0} & {3} \\ \hline 2 & {4} & {0} & {2} \\ \hline\end{array}$$

What is MSwithin?

Heena Haldankar
Heena Haldankar
Numerade Educator
03:35

Problem 22

Use the following information to answer the next eight exercises. Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in the table are the goals per game for the different teams. The one-way ANOVA results are shown in Table 13.14.
$$\begin{array}{|l|l|l|}\hline \text { Team } 1 & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} \\ \hline 1 & {2} & {0} & {3} \\ \hline 2 & {3} & {1} & {4} \\ \hline 0 & {2} & {1} & {4} \\ \hline 3 & {4} & {0} & {3} \\ \hline 2 & {4} & {0} & {2} \\ \hline\end{array}$$

What is the F statistic?

Heena Haldankar
Heena Haldankar
Numerade Educator
02:41

Problem 23

Use the following information to answer the next eight exercises. Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in the table are the goals per game for the different teams. The one-way ANOVA results are shown in Table 13.14.
$$\begin{array}{|l|l|l|}\hline \text { Team } 1 & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} \\ \hline 1 & {2} & {0} & {3} \\ \hline 2 & {3} & {1} & {4} \\ \hline 0 & {2} & {1} & {4} \\ \hline 3 & {4} & {0} & {3} \\ \hline 2 & {4} & {0} & {2} \\ \hline\end{array}$$

Judging by the F statistic, do you think it is likely or unlikely that you will reject the null hypothesis?

Heena Haldankar
Heena Haldankar
Numerade Educator
01:07

Problem 24

An F statistic can have what values?

Heena Haldankar
Heena Haldankar
Numerade Educator
01:42

Problem 25

What happens to the curves as the degrees of freedom for the numerator and the denominator get larger?

Heena Haldankar
Heena Haldankar
Numerade Educator
04:31

Problem 26

Use the following information to answer the next seven exercise. Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 13.15.
$$ \begin{array}{|l|l|l|l|}\hline \text { Team } & {1} & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} & {\text { Team } 5} \\ \hline 36 & {32} & {48} & {38} & {41} \\ \hline 42 & {35} & {50} & {44} & {39} \\ \hline 51 & {38} & {39} & {46} & {40} \\ \hline\end{array} $$

What is the df(num)?

Heena Haldankar
Heena Haldankar
Numerade Educator
01:55

Problem 27

Use the following information to answer the next seven exercise. Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 13.15.
$$ \begin{array}{|l|l|l|l|}\hline \text { Team } & {1} & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} & {\text { Team } 5} \\ \hline 36 & {32} & {48} & {38} & {41} \\ \hline 42 & {35} & {50} & {44} & {39} \\ \hline 51 & {38} & {39} & {46} & {40} \\ \hline\end{array} $$

What is the df(denom)?

Heena Haldankar
Heena Haldankar
Numerade Educator
01:27

Problem 28

Use the following information to answer the next seven exercise. Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 13.15.
$$ \begin{array}{|l|l|l|l|}\hline \text { Team } & {1} & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} & {\text { Team } 5} \\ \hline 36 & {32} & {48} & {38} & {41} \\ \hline 42 & {35} & {50} & {44} & {39} \\ \hline 51 & {38} & {39} & {46} & {40} \\ \hline\end{array} $$

What are the Sum of Squares and Mean Squares Factors?

Heena Haldankar
Heena Haldankar
Numerade Educator
06:55

Problem 29

Use the following information to answer the next seven exercise. Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 13.15.
$$ \begin{array}{|l|l|l|l|}\hline \text { Team } & {1} & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} & {\text { Team } 5} \\ \hline 36 & {32} & {48} & {38} & {41} \\ \hline 42 & {35} & {50} & {44} & {39} \\ \hline 51 & {38} & {39} & {46} & {40} \\ \hline\end{array} $$

What are the Sum of Squares and Mean Squares Errors?

Trang Hoang
Trang Hoang
Numerade Educator
02:32

Problem 30

Use the following information to answer the next seven exercise. Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 13.15.
$$ \begin{array}{|l|l|l|l|}\hline \text { Team } & {1} & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} & {\text { Team } 5} \\ \hline 36 & {32} & {48} & {38} & {41} \\ \hline 42 & {35} & {50} & {44} & {39} \\ \hline 51 & {38} & {39} & {46} & {40} \\ \hline\end{array} $$

What is the F statistic?

Trang Hoang
Trang Hoang
Numerade Educator
01:48

Problem 31

Use the following information to answer the next seven exercise. Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 13.15.
$$ \begin{array}{|l|l|l|l|}\hline \text { Team } & {1} & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} & {\text { Team } 5} \\ \hline 36 & {32} & {48} & {38} & {41} \\ \hline 42 & {35} & {50} & {44} & {39} \\ \hline 51 & {38} & {39} & {46} & {40} \\ \hline\end{array} $$

What is the p-value?

Trang Hoang
Trang Hoang
Numerade Educator
01:05

Problem 32

Use the following information to answer the next seven exercise. Four basketball teams took a random sample of players regarding how high each player can jump (in inches). The results are shown in Table 13.15.
$$ \begin{array}{|l|l|l|l|}\hline \text { Team } & {1} & {\text { Team } 2} & {\text { Team } 3} & {\text { Team } 4} & {\text { Team } 5} \\ \hline 36 & {32} & {48} & {38} & {41} \\ \hline 42 & {35} & {50} & {44} & {39} \\ \hline 51 & {38} & {39} & {46} & {40} \\ \hline\end{array} $$

At the 5% significance level, is there a difference in the mean jump heights among the teams?

Trang Hoang
Trang Hoang
Numerade Educator
00:48

Problem 33

Use the following information to answer the next seven exercises. A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in Table 13.16
$$\begin{array}{|l|l|l|}\hline \text { Group A } & {\text { Group } B} & {\text { Group } C} \\ \hline 101 & {151} & {101} \\ \hline 108 & {149} & {109} \\ \hline 98 & {160} & {198} \\ \hline 107 & {112} & {186} \\ \hline 111 & {126} & {160} \\ \hline\end{array}$$

What is the df(num)?

Trang Hoang
Trang Hoang
Numerade Educator
01:06

Problem 34

Use the following information to answer the next seven exercises. A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in Table 13.16
$$\begin{array}{|l|l|l|}\hline \text { Group A } & {\text { Group } B} & {\text { Group } C} \\ \hline 101 & {151} & {101} \\ \hline 108 & {149} & {109} \\ \hline 98 & {160} & {198} \\ \hline 107 & {112} & {186} \\ \hline 111 & {126} & {160} \\ \hline\end{array}$$

What is the df(denom)

Trang Hoang
Trang Hoang
Numerade Educator
03:28

Problem 35

Use the following information to answer the next seven exercises. A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in Table 13.16
$$\begin{array}{|l|l|l|}\hline \text { Group A } & {\text { Group } B} & {\text { Group } C} \\ \hline 101 & {151} & {101} \\ \hline 108 & {149} & {109} \\ \hline 98 & {160} & {198} \\ \hline 107 & {112} & {186} \\ \hline 111 & {126} & {160} \\ \hline\end{array}$$

What are the SS between and MS between?

Trang Hoang
Trang Hoang
Numerade Educator
02:19

Problem 36

Use the following information to answer the next seven exercises. A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in Table 13.16
$$\begin{array}{|l|l|l|}\hline \text { Group A } & {\text { Group } B} & {\text { Group } C} \\ \hline 101 & {151} & {101} \\ \hline 108 & {149} & {109} \\ \hline 98 & {160} & {198} \\ \hline 107 & {112} & {186} \\ \hline 111 & {126} & {160} \\ \hline\end{array}$$

What are the SSwithin and MSwithin?

Trang Hoang
Trang Hoang
Numerade Educator
00:53

Problem 37

Use the following information to answer the next seven exercises. A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in Table 13.16
$$\begin{array}{|l|l|l|}\hline \text { Group A } & {\text { Group } B} & {\text { Group } C} \\ \hline 101 & {151} & {101} \\ \hline 108 & {149} & {109} \\ \hline 98 & {160} & {198} \\ \hline 107 & {112} & {186} \\ \hline 111 & {126} & {160} \\ \hline\end{array}$$

What is the F Statistic?

Trang Hoang
Trang Hoang
Numerade Educator
01:05

Problem 38

Use the following information to answer the next seven exercises. A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in Table 13.16
$$\begin{array}{|l|l|l|}\hline \text { Group A } & {\text { Group } B} & {\text { Group } C} \\ \hline 101 & {151} & {101} \\ \hline 108 & {149} & {109} \\ \hline 98 & {160} & {198} \\ \hline 107 & {112} & {186} \\ \hline 111 & {126} & {160} \\ \hline\end{array}$$

What is the p-value?

Trang Hoang
Trang Hoang
Numerade Educator
00:44

Problem 39

Use the following information to answer the next seven exercises. A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in Table 13.16
$$\begin{array}{|l|l|l|}\hline \text { Group A } & {\text { Group } B} & {\text { Group } C} \\ \hline 101 & {151} & {101} \\ \hline 108 & {149} & {109} \\ \hline 98 & {160} & {198} \\ \hline 107 & {112} & {186} \\ \hline 111 & {126} & {160} \\ \hline\end{array}$$

At the 10% significance level, are the scores among the different groups different?

Trang Hoang
Trang Hoang
Numerade Educator
09:06

Problem 40

Use the following information to answer the next three exercises. Suppose a group is interested in determining whetherteenagers obtain their drivers licenses at approximately the sameaverage age across the country. Suppose that the following
data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.
TABLE CANNOT COPY.
Enter the data into your calculator or computer.

p-value = ______

Trang Hoang
Trang Hoang
Numerade Educator
01:56

Problem 41

Use the following information to answer the next three exercises. Suppose a group is interested in determining whetherteenagers obtain their drivers licenses at approximately the sameaverage age across the country. Suppose that the following
data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.
TABLE CANNOT COPY.
Enter the data into your calculator or computer.

State the decisions and conclusions (in complete sentences) for the following preconceived levels of ?.
? = 0.05
a. Decision: ____________________________
b. Conclusion: ____________________________

Trang Hoang
Trang Hoang
Numerade Educator
02:11

Problem 42

interested in determining whetherteenagers obtain their drivers licenses at approximately the sameaverage age across the country. Suppose that the following
data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.
TABLE CANNOT COPY.
Enter the data into your calculator or computer.

? = 0.01
a. Decision: ____________________________
b. Conclusion: ____________________________

Trang Hoang
Trang Hoang
Numerade Educator
00:57

Problem 43

Use the following information to answer the next three exercises. Suppose a group is Use the following information to answer the next two exercises. There are two assumptions that must be true in order to perform an F test of two variances.

Name one assumption that must be true.

Trang Hoang
Trang Hoang
Numerade Educator
00:51

Problem 44

Use the following information to answer the next three exercises. Suppose a group is Use the following information to answer the next two exercises. There are two assumptions that must be true in order to perform an F test of two variances.

What is the other assumption that must be true?

Trang Hoang
Trang Hoang
Numerade Educator
01:24

Problem 45

Use the following information to answer the next five exercises. Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker’s times have a variance of 12.1. The second worker’s times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times and that his commute time is shorter. Test the claim at the 10% level

State the null and alternative hypotheses

Trang Hoang
Trang Hoang
Numerade Educator
00:29

Problem 46

Use the following information to answer the next five exercises. Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker’s times have a variance of 12.1. The second worker’s times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times and that his commute time is shorter. Test the claim at the 10% level

What is s1 in this problem?

Trang Hoang
Trang Hoang
Numerade Educator
00:36

Problem 47

Use the following information to answer the next five exercises. Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker’s times have a variance of 12.1. The second worker’s times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times and that his commute time is shorter. Test the claim at the 10% level

What is s2 in this problem?

Trang Hoang
Trang Hoang
Numerade Educator
00:44

Problem 48

Use the following information to answer the next five exercises. Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker’s times have a variance of 12.1. The second worker’s times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times and that his commute time is shorter. Test the claim at the 10% level

What is n?

Trang Hoang
Trang Hoang
Numerade Educator
00:48

Problem 49

Use the following information to answer the next five exercises. Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker’s times have a variance of 12.1. The second worker’s times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times and that his commute time is shorter. Test the claim at the 10% level

What is the F statistic?

Trang Hoang
Trang Hoang
Numerade Educator
01:07

Problem 50

Use the following information to answer the next five exercises. Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker’s times have a variance of 12.1. The second worker’s times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times and that his commute time is shorter. Test the claim at the 10% level

What is the p-value?

Trang Hoang
Trang Hoang
Numerade Educator
01:24

Problem 51

Use the following information to answer the next five exercises. Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for 20 commutes. The first worker’s times have a variance of 12.1. The second worker’s times have a variance of 16.9. The first worker thinks that he is more consistent with his commute times and that his commute time is shorter. Test the claim at the 10% level

Is the claim accurate?

Trang Hoang
Trang Hoang
Numerade Educator
00:43

Problem 52

Use the following information to answer the next four exercises. Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they have taken so far. The first student’s grades have a standard deviation of 38.1. The second student’s grades have a standard deviation of 22.5. The second student thinks his scores are lower.

State the null and alternative hypotheses.

Trang Hoang
Trang Hoang
Numerade Educator
01:02

Problem 53

Use the following information to answer the next four exercises. Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they have taken so far. The first student’s grades have a standard deviation of 38.1. The second student’s grades have a standard deviation of 22.5. The second student thinks his scores are lower.

What is the F Statistic?

Trang Hoang
Trang Hoang
Numerade Educator
01:12

Problem 54

Use the following information to answer the next four exercises. Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they have taken so far. The first student’s grades have a standard deviation of 38.1. The second student’s grades have a standard deviation of 22.5. The second student thinks his scores are lower.

What is the p-value?

Trang Hoang
Trang Hoang
Numerade Educator
00:52

Problem 55

Use the following information to answer the next four exercises. Two students are interested in whether or not there is variation in their test scores for math class. There are 15 total math tests they have taken so far. The first student’s grades have a standard deviation of 38.1. The second student’s grades have a standard deviation of 22.5. The second student thinks his scores are lower.

At the 5% significance level, do we reject the null hypothesis?

Trang Hoang
Trang Hoang
Numerade Educator
01:05

Problem 56

Use the following information to answer the next three exercises. Two cyclists are comparing the variances of their overall paces going uphill. Each cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of 23.8 and the second cyclist has a variance of 32.1. The cyclists want to see if their variances are the same or different.

State the null and alternative hypotheses.

Trang Hoang
Trang Hoang
Numerade Educator
00:59

Problem 57

Use the following information to answer the next three exercises. Two cyclists are comparing the variances of their overall paces going uphill. Each cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of 23.8 and the second cyclist has a variance of 32.1. The cyclists want to see if their variances are the same or different.

What is the F Statistic?

Trang Hoang
Trang Hoang
Numerade Educator
01:53

Problem 58

Use the following information to answer the next three exercises. Two cyclists are comparing the variances of their overall paces going uphill. Each cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of 23.8 and the second cyclist has a variance of 32.1. The cyclists want to see if their variances are the same or different.

At the 5% significance level, what can we say about the cyclists’ variances?

Trang Hoang
Trang Hoang
Numerade Educator
01:37

Problem 59

Three different traffic routes are tested for mean driving time. The entries in the table are the driving times in minutes on the three different routes. The one-way ANOVA results are shown in Table 13.18.
$$\begin{array}{|l|l|l|}\hline \text { Route 1 } & {\text { Route } 2} & {\text { Route } 3} \\ \hline 30 & {27} & {16} \\ \hline 32 & {29} & {41} \\ \hline 27 & {28} & {22} \\ \hline 35 & {36} & {31} \\ \hline\end{array}$$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:46

Problem 60

Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.
TABLE CANNOT COPY.
State the hypotheses.
H0: ____________
Ha: ____________

Trang Hoang
Trang Hoang
Numerade Educator
01:27

Problem 61

same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which
teenagers obtained their drivers licenses.
TABLE CANNOT COPY.
$$\begin{array}{l}{H_{0} : \mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}=\mu_{5}} \\ {H \alpha : \text { At least any two of the group means } \mu_{1}, \mu_{2}, \ldots, \mu_{5} \text { are not equal. }}\end{array}$$

degrees of freedom – numerator: df(num) = _________

Nick Johnson
Nick Johnson
Numerade Educator
09:06

Problem 62

Use the following information to answer the next three exercises. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which
teenagers obtained their drivers licenses.
TABLE CANNOT COPY.
$$\begin{array}{l}{H_{0} : \mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}=\mu_{5}} \\ {H \alpha : \text { At least any two of the group means } \mu_{1}, \mu_{2}, \ldots, \mu_{5} \text { are not equal. }}\end{array}$$

degrees of freedom – denominator: df(denom) = ________

Trang Hoang
Trang Hoang
Numerade Educator
09:06

Problem 63

Use the following information to answer the next three exercises. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which
teenagers obtained their drivers licenses.
TABLE CANNOT COPY.
$$\begin{array}{l}{H_{0} : \mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}=\mu_{5}} \\ {H \alpha : \text { At least any two of the group means } \mu_{1}, \mu_{2}, \ldots, \mu_{5} \text { are not equal. }}\end{array}$$

F statistic = ________

Trang Hoang
Trang Hoang
Numerade Educator
07:07

Problem 64

Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain.
$$\begin{array}{|c|c|c|}\hline \text { Linda's rats } & {\text { Tuan's rats }} & {\text { Javier's rats }} \\ \hline 43.5 & {47.0} & {51.2} \\ \hline 39.4 & {40.5} & {40.9} \\ \hline 41.3 & {38.9} & {37.9} \\ \hline 46.0 & {46.3} & {45.0} \\ \hline 38.2 & {44.2} & {48.6} \\ \hline\end{array}$$

Nick Johnson
Nick Johnson
Numerade Educator
01:17

Problem 65

A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are in Table 13.22. Using a 5% significance level, test the hypothesis that the three mean commuting mileages are the same.
TABLE CANNOT COPY

Adriano Chikande
Adriano Chikande
Numerade Educator
03:09

Problem 66

Using a significance level of $5 \%$, test the hypothesis that the four magazine types have the same mean length.

Beth Stone
Beth Stone
Numerade Educator
03:09

Problem 67

Using a significance level of 5%, test the hypothesis that the four magazine types have the same mean length.

Beth Stone
Beth Stone
Numerade Educator
02:04

Problem 68

A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose that Table 13.24 shows the results of a study.
Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of $0.05 .$

Alexander Cheng
Alexander Cheng
Numerade Educator
02:04

Problem 69

A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose that Table 13.24 shows the results of a study.
$$\begin{array}{|c|c|c|}\hline \text { CNN } & {\text { FOX }} & {\text { Local }} \\ \hline 45 & {15} & {72} \\ \hline 12 & {43} & {37} \\ \hline 18 & {68} & {56} \\ \hline 38 & {50} & {60} \\ \hline 23 & {31} & {51} \\ \hline 35 & {22} & {} \\ \hline\end{array}$$
Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

Alexander Cheng
Alexander Cheng
Numerade Educator
02:01

Problem 70

Are the means for the final exams the same for all statistics class delivery types? Table 13.25 shows the scores on final exams from several randomly selected classes that used the different delivery types.
TABLE CANNOT COPY
Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:04

Problem 71

Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that Table 13.26 shows the results of a study.
$$\begin{array}{|c|c|c|c|}\hline \text { White } & {\text { Black }} & {\text { Hispanic }} & {\text { Asian }} \\ \hline 6 & {4} & {7} & {8} \\ \hline 8 & {1} & {3} & {3} \\ \hline 2 & {5} & {5} & {5} \\ \hline 4 & {2} & {4} & {1} \\ \hline 6 & {} & {6} & {7} \\ \hline\end{array}$$
Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

Alexander Cheng
Alexander Cheng
Numerade Educator
02:04

Problem 72

Are the mean numbers of daily visitors to a ski resort the same for the three types of snow conditions? Suppose that Table 13.27 shows the results of a study.
$$\begin{array}{|c|c|c|}\hline \text { Powder } & {\text { Machine Made }} & {\text { Hard Packed }} \\ \hline 1,210 & {2,107} & {2,846} \\ \hline 1,080 & {1,149} & {1,638} \\ \hline 1,537 & {862} & {2,019} \\ \hline 941 & {1,870} & {1,178} \\ \hline & {1,528} & {2,233} \\ \hline & {1,382} & {} \\ \hline\end{array}$$
Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

Alexander Cheng
Alexander Cheng
Numerade Educator
01:22

Problem 73

DDT is a pesticide that has been banned from use in the United States and most other areas of the world. It is quite effective, but persisted in the environment and over time became seen as harmful to higher-level organisms. Famously, egg shells of eagles and other raptors were believed to be thinner and prone to breakage in the nest because of ingestion of DDT in the food chain of the birds. An experiment was conducted on the number of eggs (fecundity) laid by female fruit flies. There are three groups of flies. One group was bred to be resistant to DDT (the RS group). Another was bred to be especially susceptible to DDT (SS). Finally there was a control line of non-selected or typical fruitflies (NS). Here are the data:
$$
\begin{array}{|l|l|l|l|l|l|}
\hline \text { RS } & \text { SS } & \text { NS } & \text { RS } & \text { SS } & \text { NS } \\
\hline 12.8 & 38.4 & 35.4 & 22.4 & 23.1 & 22.6 \\
\hline 21.6 & 32.9 & 27.4 & 27.5 & 29.4 & 40.4 \\
\hline 14.8 & 48.5 & 19.3 & 20.3 & 16 & 34.4 \\
\hline 23.1 & 20.9 & 41.8 & 38.7 & 20.1 & 30.4 \\
\hline 34.6 & 11.6 & 20.3 & 26.4 & 23.3 & 14.9 \\
\hline 19.7 & 22.3 & 37.6 & 23.7 & 22.9 & 51.8 \\
\hline 22.6 & 30.2 & 36.9 & 26.1 & 22.5 & 33.8 \\
\hline 29.6 & 33.4 & 37.3 & 29.5 & 15.1 & 37.9 \\
\hline 16.4 & 26.7 & 28.2 & 38.6 & 31 & 29.5 \\
\hline 20.3 & 39 & 23.4 & 44.4 & 16.9 & 42.4 \\
\hline 29.3 & 12.8 & 33.7 & 23.2 & 16.1 & 36.6 \\
\hline 14.9 & 14.6 & 29.2 & 23.6 & 10.8 & 47.4 \\
\hline 27.3 & 12.2 & 41.7 & & & \\
\hline
\end{array}
$$

Dominador Tan
Dominador Tan
Numerade Educator
01:22

Problem 74

DDT is a pesticide that has been banned from use in the United States and most other areas of the world. It is quite effective, but persisted in the environment and over time became seen as harmful to higher-level organisms. Famously, egg shells of eagles and other raptors were believed to be thinner and prone to breakage in the nest because of ingestion of DDT in the food chain of the birds.
An experiment was conducted on the number of eggs (fecundity) laid by female fruit flies. There are three groups of flies. One group was bred to be resistant to DDT (the RS group). Another was bred to be especially susceptible to DDT (SS). Finally there was a control line of non-selected or typical fruitflies (NS). Here are the data:
TABLE CANNOT COPY
The values are the average number of eggs laid daily for each of 75 flies (25 in each group) over the first 14 days of their lives. Using a 1% level of significance, are the mean rates of egg selection for the three strains of fruitfly different? If so, in what way? Specifically, the researchers were interested in whether or not the selectively bred strains were different from the nonselected line, and whether the two selected lines were different from each other. Here is a chart of the three groups:

Dominador Tan
Dominador Tan
Numerade Educator
07:07

Problem 75

Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again and the net gain in grams is recorded.
$$\begin{array}{|l|l|l|}\hline \text { Linda's rats } & \text { Tuan's rats } & \text { Javier's rats } \\\hline 43.5 & 47.0 & 51.2 \\\hline 39.4 & 40.5 & 40.9 \\\hline 41.3 & 38.9 & 37.9 \\\hline 46.0 & 46.3 & 45.0 \\\hline 38.2 & 44.2 & 48.6 \\\hline\end{array}$$
Determine whether or not the variance in weight gain is statistically the same among Javier's and Linda's rats. Test at a significance level of $10 \%$

Nick Johnson
Nick Johnson
Numerade Educator
07:07

Problem 76

Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat’s weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again and the net gain in grams is recorded.
$$\begin{array}{|l|l|l|}\hline \text { Linda's rats } & {\text { Tuan's rats }} & {\text { Javier's rats }} \\ \hline 43.5 & {47.0} & {51.2} \\ \hline 39.4 & {40.5} & {40.9} \\ \hline 41.3 & {38.9} & {37.9} \\ \hline 46.0 & {46.3} & {45.0} \\ \hline 38.2 & {44.2} & {48.6} \\ \hline\end{array}$$
Determine whether or not the variance in weight gain is statistically the same among Javier’s and Linda’s rats. Test at a significance level of 10%.

Nick Johnson
Nick Johnson
Numerade Educator
02:02

Problem 77

Which two magazine types do you think have the same variance in length?

Ryan Mcalister
Ryan Mcalister
Numerade Educator
00:09

Problem 78

Which two magazine types do you think have different variances in length?

Maxime Rossetti
Maxime Rossetti
Numerade Educator
02:02

Problem 79

Which two magazine types do you think have the same variance in length?

Ryan Mcalister
Ryan Mcalister
Numerade Educator
00:09

Problem 80

Which two magazine types do you think have different variances in length?

Maxime Rossetti
Maxime Rossetti
Numerade Educator
04:29

Problem 81

Is the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall? Suppose that the Table 13.34 shows the results of a study.
TABLE CANNOT COPY

Jerelyn Nevil
Jerelyn Nevil
Numerade Educator
01:45

Problem 82

Are the variances for incomes on the East Coast and the West Coast the same? Suppose that Table 13.35 shows the results of a study. Income is shown in thousands of dollars. Assume that both distributions are normal. Use a level of significance of 0.05.
TABLE CANNOT COPY

Jon Southam
Jon Southam
Numerade Educator
02:53

Problem 83

Thirty men in college were taught a method of finger tapping. They were randomly assigned to three groups of ten, with each receiving one of three doses of caffeine: 0 mg, 100 mg, 200 mg. This is approximately the amount in no, one, or two cups of coffee. Two hours after ingesting the caffeine, the men had the rate of finger tapping per minute recorded. The experiment was double blind, so neither the recorders nor the students knew which group they were in. Does caffeine affect the rate of tapping, and if so how? Here are the data:
$$ \begin{array}{|l|l|l|l|l|}\hline 0 \mathrm{mg} & {100 \mathrm{mg}} & {200 \mathrm{mg}} & {0 \mathrm{mg}} & {100 \mathrm{mg}} & {200 \mathrm{mg}} \\ \hline 242 & {248} & {246} & {245} & {246} & {248} \\ \hline 244 & {245} & {250} & {248} & {247} & {252} \\ \hline 247 & {248} & {248} & {248} & {250} & {250} \\ \hline 242 & {247} & {246} & {244} & {246} & {248} \\ \hline 246 & {243} & {245} & {242} & {244} & {250} \\ \hline\end{array} $$

Lucas Finney
Lucas Finney
Numerade Educator
02:10

Problem 84

King Manuel I, Komnenus ruled the Byzantine Empire from Constantinople (Istanbul) during the years 1145 to 1180 A.D. The empire was very powerful during his reign, but declined significantly afterwards. Coins minted during his era were found in Cyprus, an island in the eastern Mediterranean Sea. Nine coins were from his first coinage, seven from the second, four from the third, and seven from a fourth. These spanned most of his reign. We have data on the silver content of the coins:
TABLE CANNOT COPY

Xiaomin Bian
Xiaomin Bian
Numerade Educator
01:44

Problem 85

The American League and the National League of Major League Baseball are each divided into three divisions: East, Central, and West. Many years, fans talk about some divisions being stronger (having better teams) than other divisions. This may have consequences for the postseason. For instance, in 2012 Tampa Bay won 90 games and did not play in the postseason, while Detroit won only 88 and did play in the postseason. This may have been an oddity, but is there good evidence that in the 2012 season, the American League divisions were significantly different in overall records? Use the following data to test whether the mean number of wins per team in the three American League divisions were the same or not. Note that the data are not balanced, as two divisions had five teams, while one had only four.
TABLE CANNOT COPY

Brandon Cleary
Brandon Cleary
Numerade Educator