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...

Extracted 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.