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Chapter 12: Q7BSC (page 566)

The heights (cm) in the following table are from Data Set 1 鈥淏ody Data鈥� in Appendix B. Results from two-way analysis of variance are also shown. Use the displayed results and use a 0.05 significance level. What do you conclude?


Female

Male

18-29

161.2

170.2

162.9

155.5

168

153.3

152

154.9

157.4

159.5

172.8

178.7

183.1

175.9

161.8

177.5

170.5

180.1

178.6

30-49

169.1

170.6

171.1

159.6

169.8

169.5

156.5

164

164.8

155

170.1

165.4

178.5

168.5

180.3

178.2

174.4

174.6

162.8

50-80

146.7

160.9

163.3

176.1

163.1

151.6

164.7

153.3

160.3

134.5

181.9

166.6

171.7

170

169.1

182.9

176.3

166.7

166.3

Short Answer

Expert verified

The following conclusions can be drawn.

  • The interaction between age and gender does not have a significant effect on the heights of the subjects.
  • The factor of age does not have a significant effect on the heights of the subjects.
  • The factor of gender has a significant effect on the heights of the subjects.

Step by step solution

01

Given information

The ANOVA table is provided for the data given on heights (cm) under two factors: age bracket and gender.

02

Testing the interaction effect

For the given two-way analysis of variance, the following hypotheses are set up.

Null hypothesis: There is no interaction effect between age and gender on heights.

Alternative hypothesis: There is an interaction effect between age and gender on heights.

The ANOVA output shows that the p-value corresponding to the F-statistic value of 1.7970 (under interaction), that is, the row with the header Age*Gender is equal to 0.1756.

As the p-value is greater than 0.05, the null hypothesis is failed to be rejected.

Thus, it can be concluded at 0.05 that there is no sufficient evidence that there exists an interaction between the factors of age and gender on height.

As the interaction effect is not significant, the individual effects of age and gender will be tested.

03

Testing the effect of the factor ‘age’

The following hypotheses are set up to test the effect of age on heights.

Null hypothesis: There is no significant effect of age on heights.

Alternative hypothesis: There is a significant effect of age on heights.

The ANOVA output shows that the p-value corresponding to the F-statistic value (under age) of 2.0403 is equal to 0.1399 (from the row header 鈥楢ge鈥�).

As the p-value is greater than 0.05, the null hypothesis is failed to be rejected.

It can be concluded that there is no significant evidence to conclude the effect of age on heights.

04

Testing the effect of the factor ‘gender’

The following hypotheses are set up to test the effect of gender on heights.

Null hypothesis: There is no significant effect of gender on heights.

Alternative hypothesis: There is a significant effect of gender on heights.

The ANOVA output shows that the p-value corresponding to the F-statistic value (under gender) of 43.4607 is less than 0.0001 (from the row header 鈥楪ender鈥�).

As the p-value is less than 0.05, the null hypothesis is rejected.

It can be concluded that there is a significant effect of gender on heights.

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Most popular questions from this chapter

Fast Food Dinner Service Times Data Set 25 鈥淔ast Food鈥� in Appendix B lists drivethrough service times (seconds) for dinners at McDonald鈥檚, Burger King, and Wendy鈥檚. 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?

Estimating Length Using the same results displayed in Exercise 8, does it appear that the length estimates are affected by the sex of the subject?

Pancake Experiment Listed below are ratings of pancakes made by experts (based on data from Minitab). Different pancakes were made with and without a supplement and with different amounts of whey. The results from two-way analysis of variance are shown. Use the displayed results and a 0.05 significance level. What do you conclude?

Whey


0%

10%

20%

30%

No Supplement

4.4

4.5

4.3

4.6

4.5

4.8

4.5

4.8

4.8

4.6

4.7

5.1

Supplement

3.3

3.2

3.1

3.8

3.7

3.6

5.0

5.3

4.8

5.4

5.6

5.3

Cola Weights For the four samples described in Exercise 1, the sample of regular Coke has a mean weight of 0.81682 lb, the sample of Diet Coke has a mean weight of 0.78479 lb, the sample of regular Pepsi has a mean weight of 0.82410 lb, and the sample of Diet Pepsi has a mean weight of 0.78386 lb. If we use analysis of variance and reach a conclusion to reject equality of the four sample means, can we then conclude that any of the specific samples have means that are significantly different from the others?

Flight Departure Delays Listed below are departure delay times (minutes) for American Airlines 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?

Flight 1

-2

-1

-2

2

-2

0

-2

-3

Flight 19

19

-4

-5

-1

-4

73

0

1

Flight21

18

60

142

-1

-11

-1

47

13
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