An athletic shoemaker wants to test if their new running shoe specially made for sprinting is better than the competition. To do this, they recruit 35 NCAA sprinters and time their 100-meter dash wearing the company's shoe and then time their 100-meter dash again wearing the competitor’s shoe. The difference of these times is then calculated asTimecompany.shoe−Timecompetitor.shoe. The sample mean difference in times is 0.53 seconds and the sample standard deviation is 1.1. Conduct a hypothesis test at theα=0.1 level. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in the context of the problem) (b) Calculate the test statistic (c) Calculate the critical value.
An athletic shoemaker wants to test if their new running shoe specially made for sprinting is better than the competition. To do this, they recruit 35 NCAA sprinters and time their 100-meter dash wearing the company's shoe and then time their 100-meter dash again wearing the competitor’s shoe. The difference of these times is then calculated asTimecompany.shoe−Timecompetitor.shoe. The sample mean difference in times is 0.53 seconds and the sample standard deviation is 1.1. Conduct a hypothesis test at theα=0.1 level.
(a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in the context of the problem)
(b) Calculate the test statistic
(c) Calculate the critical value.
(d) Draw a picture of the distribution of the test statistic underH0. Label and provide values for the critical value and the test statistic, and shade the critical region.
(e) Make and justify a statistical decision at theα= 0.15 level and state your conclusions in the context of the problem.
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