Elementary Statistics

Mario F. Triola

Chapter 12

Analysis of Variance - all with Video Answers

Educators

Section 1

One-Way ANOVA

Problem 1

Use the following listed arrival delay times (minutes) for American Airline flights from New York to Los Angeles. Negative values correspond to flights that arrived early. Also shown are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different flights have the same mean arrival delay time. (FIGURE CAN'T COPY)(FIGURE CAN'T COPY)
ANOVA
a. What characteristic of the data above indicates that we should use one-way analysis of variance?
b. If the objective is to test the claim that the three flights have the same mean arrival delay time, why is the method referred to as analysis of variance?

Sheryl Ezze

Sheryl Ezze

Numerade Educator

Problem 2

Use the following listed arrival delay times (minutes) for American Airline flights from New York to Los Angeles. Negative values correspond to flights that arrived early. Also shown are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different flights have the same mean arrival delay time. (FIGURE CAN'T COPY)(FIGURE CAN'T COPY)
Why Not Test Two at a Time? Refer to the sample data given in Exercise 1. If we want to test for equality of the three means, why don't we use three separate hypothesis tests for $\mu_{1}=\mu_{2}, \mu_{1}=\mu_{3},$ and $\mu_{2}=\mu_{3} ?$

Sheryl Ezze

Numerade Educator

Problem 3

Use the following listed arrival delay times (minutes) for American Airline flights from New York to Los Angeles. Negative values correspond to flights that arrived early. Also shown are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different flights have the same mean arrival delay time. (FIGURE CAN'T COPY)(FIGURE CAN'T COPY)
Test Statistic What is the value of the test statistic? What distribution is used with the test statistic?

Sheryl Ezze

Numerade Educator

Problem 4

Use the following listed arrival delay times (minutes) for American Airline flights from New York to Los Angeles. Negative values correspond to flights that arrived early. Also shown are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different flights have the same mean arrival delay time. (FIGURE CAN'T COPY)(FIGURE CAN'T COPY)
P-value If we use a 0.05 significance level in analysis of variance with the sample data given in Exercise $1,$ what is the $P$ -value? What should we conclude? If a passenger abhors late flight arrivals, can that passenger be helped by selecting one of the flights?

Sheryl Ezze

Numerade Educator

Problem 5

Use analysis of variance for the indicated test.
Lead and Verbal IQ Scores Example 1 used measured performance IQ scores for three different blood lead levels. If we use the same three categories of blood lead levels with measured verbal IQ scores, we get the accompanying Minitab display. (The data are listed in Data Set 7 "IQ and Lead" in Appendix B.) Using a 0.05 significance level, test the claim that the three categories of blood lead level have the same mean verbal IQ score. Does exposure to lead appear to have an effect on verbal IQ scores? (TABLE CAN'T COPY)

Sheryl Ezze

Numerade Educator

Problem 6

Use analysis of variance for the indicated test.
Lead and Full IQ Scores Example 1 used measured performance IQ scores for three different blood lead levels. If we use the same three categories of blood lead levels with the full IQ scores, we get the accompanying Excel display. (The data are listed in Data Set 7 "IQ and Lead" in Appendix B.) Using a 0.05 significance level, test the claim that the three categories of blood lead level have the same mean full IQ score. Does it appear that exposure to lead has an effect on full IQ scores?(TABLE CAN'T COPY)

Sheryl Ezze

Numerade Educator

Problem 7

Use analysis of variance for the indicated test.
Fast Food Dinner Service Times Data Set 25 "Fast Food" in Appendix B lists drivethrough service times (seconds) for dinners at McDonald's, Burger King, and Wendy's. Using those times with a TI- $83 / 84$ Plus calculator yields the following display. Using a 0.05 significance level, test the claim that the three samples are from populations with the same mean. What do you conclude? (TABLE CAN'T COPY)

Sheryl Ezze

Numerade Educator

Problem 8

Use analysis of variance for the indicated test.
Birth Weights Data Set 4 "Births" in Appendix B lists birth weights from babies born at Albany Medical Center, Bellevue Hospital in New York City, Olean General Hospital, and Strong Memorial Hospital in Rochester, New York. After partitioning the birth weights according to the hospital, we get the StatCrunch display shown here. Use a 0.05 significance level to test the claim that the different hospitals have different mean birth weights. Do birth weights appear to be different in urban and rural areas? (TABLE CAN'T COPY)

Janet Meinke

Numerade Educator

Problem 9

Use analysis of variance for the indicated test.
Female Pulse Rates and Age Using the pulse rates of females from Data Set 1 "Body Data" in Appendix B after they are partitioned into the three age brackets of $18-25,26-40,$ and $41-80,$ we get the following Statdisk display. Using a 0.05 significance level, test the claim that females from the three age brackets have the same mean pulse rate. What do you conclude? (TABLE CAN'T COPY)

Sheryl Ezze

Numerade Educator

Problem 10

Use analysis of variance for the indicated test.
Male Pulse Rates and Age Using the pulse rates of males from Data Set 1 "Body Data" in Appendix $\mathrm{B}$ after they are partitioned into the three age brackets of $18-25,26-40,$ and $41-80,$ we get the following SPSS display. Using a 0.05 significance level, test the claim that males from the three age brackets have the same mean pulse rate. What do you conclude? (TABLE CAN'T COPY)

Sheryl Ezze

Numerade Educator

Problem 11

Use analysis of variance for the indicated test.
Triathlon Times Jeff Parent is a statistics instructor who participates in triathlons. Listed below are times (in minutes and seconds) he recorded while riding a bicycle for five stages through each mile of a 3 -mile loop. Use a 0.05 significance level to test the claim that it takes the same time to ride each of the miles. Does one of the miles appear to have a hill? (TABLE CAN'T COPY)

Sheryl Ezze

Numerade Educator

Problem 12

Use analysis of variance for the indicated test.
Arsenic in Rice Listed below are amounts of arsenic in samples of brown rice from three different states. The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. Do the amounts of arsenic appear to be different in the different states? Given that the amounts of arsenic in the samples from Texas have the highest mean, can we conclude that brown rice from Texas poses the greatest health problem? (TABLE CAN'T COPY)

Harsh Gadhiya

Numerade Educator

Problem 13

Use analysis of variance for the indicated test.
Flight Departure Delays Listed below are departure delay times (minutes) for American Airline flights from New York to Los Angeles. Negative values correspond to flights that departed early. Use a 0.05 significance level to test the claim that the different flights have the same mean departure delay time. What notable feature of the data can be identified by visually examining the data? (TABLE CAN'T COPY)

Sheryl Ezze

Numerade Educator

Problem 14

Use analysis of variance for the indicated test.
Speed Dating Listed below are attribute ratings of males by females who participated in speed dating events (from Data Set 18 "Speed Dating" in Appendix B). Use a 0.05 significance level to test the claim that females in the different age brackets give attribute ratings with the same mean. Does age appear to be a factor in the female attribute ratings? (TABLE CAN'T COPY)

Sheryl Ezze

Numerade Educator

Problem 15

Use the data set in Appendix $B$.
Chocolate Chip Cookies Refer to Data Set 28 "Chocolate Chip Cookies" in Appendix B and use the counts of chocolate chips from the three different types of Chips Ahoy cookies. Use a 0.05 significance level to test the claim that the three different types of Chips Ahoy cookies have the same mean number of chocolate chips. Do the reduced fat Chips Ahoy cookies appear to have fewer chocolate chips?

Jeff Vermeire

Numerade Educator

Problem 16

Use the data set in Appendix $B$.
Secondhand Smoke Refer to Data Set 12 "Passive and Active Smoke" in Appendix B and use the measured serum cotinine levels (in $\mathrm{mg} / \mathrm{mL}$ ) from the three groups of subjects (smokers, nonsmokers exposed to tobacco smoke, and nonsmokers not exposed to tobacco smoke). When nicotine is absorbed by the body, cotinine is produced. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. What do the results suggest about the effects of secondhand smoke?

Sheryl Ezze

Numerade Educator

Problem 17

Tukey Test A display of the Bonferroni test results from Table $12-1$ (which is part of the Chapter Problem) is provided on page $577 .$ Shown on the top of the next page is the SPSS-generated display of results from the Tukey test using the same data. Compare the Tukey test results to those from the Bonferroni test. (TABLE CAN'T COPY)

Victor Salazar

Numerade Educator

Problem 18

Bonferroni Test Shown below are weights (kg) of poplar trees obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the table below. The data are from a study conducted by researchers at Pennsylvania State University and were provided by Minitab, Inc. Also shown are partial results from using the Bonferroni test with the sample data. (TABLE CAN'T COPY) a. Use a 0.05 significance level to test the claim that the different treatments result in the same mean weight.
b. What do the displayed Bonferroni SPSS results tell us?
c. Use the Bonferroni test procedure with a 0.05 significance level to test for a significant difference between the mean amount of the irrigation treatment group and the group treated with both fertilizer and irrigation. Identify the test statistic and either the $P$ -value or critical values. What do the results indicate? (TABLE CAN'T COPY)

Victor Salazar

Numerade Educator