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Chapter 12: Q3CQQ (page 566)

Cola Weights Identify the value of the test statistic in the display included with Exercise 1. In general, do larger test statistics result in larger P-values, smaller P-values, or P-values that are unrelated to the value of the test statistic

Short Answer

Expert verified

The analysis of variance test defined for the four samples is a right-tailed test.

Step by step solution

01

Given information

Refer to Exercise 1 for the study to compare the mean weights of the four samples of cola using the analysis of variance method.

02

Identify the tail of the test

The tail of the test can be determined by observing the distribution of the statistic.

The statistic used in the analysis of variance test is the F-statistic following the F-distribution.

Criteria for identifying the tail of the test:

  • If the distribution of the statistic is symmetric, the test can be two-tailed or one-tailed (left-tailed or right-tailed), depending on the direction of the alternative hypothesis.
  • If the distribution of the statistic is asymmetric (skewed), the test can only be one-tailed. (It is a right-tailed test if the distribution is skewed to the right. It is a left-tailed test if the distribution is skewed to the left.)

Here, as the F-distribution is an asymmetric distribution that is skewed to the right, the analysis of variance test is a right-tailed test.

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Most popular questions from this chapter

The heights (cm) in the following table are from Data Set 1 “Body Data” 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

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

Laptop Battery Life. Consumer Reports publishes reviews and comparisons of products based on results from its laboratory. Data from their website gave the following table for battery lives, in hours, for samples of laptops made by four different computer companies. The four brands are Apple, Dell, Samsung, and Toshiba, but we have not used the names and have permuted the order.

At the 5%significance level, do the data provide sufficient evidence to conclude that a difference exists in mean battery life among the four

At the 1%significance level, do the data provide sufficient evidence to conclude that a difference exists in the mean singing rates among male Rock Sparrows exposed to the three types of breast treatments?

Cola Weights Identify the value of the test statistic in the display included with Exercise 1. In general, do larger test statistics result in larger P-values, smaller P-values, or P-values that are unrelated to the value of the test statistic?

Cola Weights Data Set 26 ‘Cola Weights and Volumes’ in Appendix B lists the weights (lb) of the contents of cans of cola from four different samples: (1) regular Coke, (2) diet Coke, (3) regular Pepsi, and (4) diet Pepsi. The results from the analysis of variance are shown on the top of the next page. What is the null hypothesis for this analysis of variance test? Based on the displayed results, what should you conclude about H0? What do you conclude about the equality of the mean weights of the four samples?
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