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Elementary Statistics

Robert Johnson, Patricia Kuby

Chapter 12

Analysis of Variance - all with Video Answers

Educators

Section 1

Introduction to the Analysis of Variance Technique

03:38

Problem 1

What information given in "The Morning Rush" on page 578 might convince you that the average commute time is significantly different in these six cities? Include in your explanation which cities might be significantly different from which other cities, which cities might not be significantly different from others, and what information led you to those conclusions.

Kayla Laughman
Kayla Laughman
Numerade Educator
05:32

Problem 2

To compare commuting times in various locations, independent random samples were obtained from the six cities presented in "The Morning Rush." The samples were from workers who commute to work during the 8: 00 a.m. rush hour.
a. Construct a graphic representation of the data using six side-by-side dotplots.
b. Visually estimate the mean commute time for each city and identify it with an X.
c. Does it appear that different cities have different effects on the average amount of time spent by workers who commute to work during the morning 8: 00 a.m. rush hour? Explain.
d. Does it visually appear that different cities have different effects on the variation in the amount of time spent by workers who commute to work during the morning 8: 00 a.m. rush hour? Explain.

Jeremiah Mbaria
Jeremiah Mbaria
Numerade Educator
04:41

Problem 3

Referring to the data in $12.2,$ is there a significant difference in the six mean one-way commute times? Explain how you might be able to show a significant difference among the means for the six cities.

Kayla Laughman
Kayla Laughman
Numerade Educator
04:41

Problem 4

a. Calculate the mean commute time for each city depicted in Exercise 12.2
b. Does there seem to be a difference among the mean one-way commute times for these six cities?
c. Calculate the standard deviation for each city's commute time.
d. Does there seem to be a difference among the standard deviations between the one-way commute times for these six cities?

Kayla Laughman
Kayla Laughman
Numerade Educator
01:12

Problem 5

Referring to the data in 12.2:
a. Construct the $95 \%$ confidence interval for the mean commute time for Atlanta and Boston.
b. Based on the confidence intervals found in part a, does it appear that the mean commute time is the same or different for these two cities? Explain.
c. Construct the $95 \%$ confidence interval for the mean commute time for Dallas.
d. $\quad$ Based on the confidence intervals found above, does it appear that the mean commute time is the same or different for Boston and Dallas? Explain.
Based on the confidence intervals found above, does it appear that the mean commute time is the same or different for the set of three cities Atlanta, Boston, and Dallas? Explain.
f. How do your confidence intervals compare to the intervals given for Atlanta, Boston, of siet alas in "The Morning Rush" on page.

Tyler Moulton
Tyler Moulton
Numerade Educator
01:53

Problem 6

Referring to the data in 12.2:
a. Construct the $95 \%$ confidence interval for the mean commute time for Philadelphia and St. Louis.
b. Based on the confidence intervals found in part a, does it appear that the mean commute time is the same or different for these two cities? Explain.
c. Construct the $95 \%$ confidence interval for the mean commute time for Seattle.
d. Based on the confidence intervals found above, does it appear that the mean commute time is the same or different for Philadelphia and Seattle? Explain.
e. Based on the confidence intervals found above, does it appear that the mean commute time is the same or different for the set of three cities Philadelphia, St. Louis, and Seattle? Explain.
f. How do your confidence intervals compare to the intervals given for Philadelphia, St. Louis,

Maxime Rossetti
Maxime Rossetti
Numerade Educator
04:36

Problem 7

Draw a dotplot of the data in Table 12.2 (p. 579 ). Represent the data using the integers $1,2,$ and $3,$ indicating the level of test factor the data are from. Do you see a "difference" among the levels?

Kayla Laughman
Kayla Laughman
Numerade Educator
02:21

Problem 8

Each department at a large industrial plant is rated weekly. State the hypotheses used to test that "The mean weekly ratings are the same in three departments."

Kayla Laughman
Kayla Laughman
Numerade Educator
07:39

Problem 9

Refer to the following ANOVA table.
a. Find the four missing values.
b. Find the calculated value for $F, F \star$

Kayla Laughman
Kayla Laughman
Numerade Educator
03:53

Problem 10

An analysis of variance experiment with level $A$ containing 10 data values; level $B, 12$ data values; level $C$,
10 values; level $D, 12$ values; level $E, 9$ values; and level $F$
10 values was analyzed using MINITAB.
a. Verify the three values for df shown on the printout. Also verify the relationship among the three numbers.
b. Verify the two MS values reported on the printout.
c. Verify the $F$ -value.
d. Verify the $p$ -value.

Beth Stone
Beth Stone
Numerade Educator