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A new brand of shoes joins the market. Sprinters are wondering which brand they should get, or if it even matter. We conduct a study to assess if there is a difference between the two brands. We recruit 24 sprinters to try on the shoes for a 100m run. 12 of them run with a pair of shoes from the first brand and we observe a sample mean of 12.975s and a sample SD of 2.71; the other 12 use the second brand and we observe a sample average of 12.825s and a sample SD of 1.93. We assume that the population of both groups follows a normal distribution but CANNOT ASSUME they have the same variance. Perform a test at the 10% significance level to assess if there is a difference between the brand means. Determine the hypothesis then run the test using either critical value OR p value approach. Do not forget to interpret your results.

A new brand of shoes joins the market. Sprinters are wondering which brand they should get, or if it even matter. We conduct a study to assess if there is a difference between the two brands. We recruit 24 sprinters to try on the shoes for a 100m run. 12 of them run with a pair of shoes from the first brand and we observe a sample mean of 12.975s and a sample SD of 2.71; the other 12 use the second brand and we observe a sample average of 12.825s and a sample SD of 1.93. We assume that the population of both groups follows a normal distribution but CANNOT ASSUME they have the same variance. Perform a test at the 10% significance level to assess if there is a difference between the brand means. Determine the hypothesis then run the test using either critical value OR p value approach. Do not forget to interpret your results.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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A new brand of shoes joins the market. Sprinters are wondering which brand they should get, or if it even matter. We conduct a study to assess if there is a difference between the two brands. We recruit 24 sprinters to try on the shoes for a 100m run. 12 of them run with a pair of shoes from the first brand and we observe a sample mean of 12.975s and a sample SD of 2.71; the other 12 use the second brand and we observe a sample average of 12.825s and a sample SD of 1.93. We assume that the population of both groups follows a normal distribution but CANNOT ASSUME they have the same variance. Perform a test at the 10% significance level to assess if there is a difference between the brand means. Determine the hypothesis then run the test using either critical value OR p value approach. Do not forget to interpret your results.
Transcribed Image Text:A new brand of shoes joins the market. Sprinters are wondering which brand they should get, or if it even matter. We conduct a study to assess if there is a difference between the two brands. We recruit 24 sprinters to try on the shoes for a 100m run. 12 of them run with a pair of shoes from the first brand and we observe a sample mean of 12.975s and a sample SD of 2.71; the other 12 use the second brand and we observe a sample average of 12.825s and a sample SD of 1.93. We assume that the population of both groups follows a normal distribution but CANNOT ASSUME they have the same variance. Perform a test at the 10% significance level to assess if there is a difference between the brand means. Determine the hypothesis then run the test using either critical value OR p value approach. Do not forget to interpret your results.
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