53. Identify the value of the TEST STATISTIC used in a hypothesis test of the following claim and sample data: Claim: "The average weekly number of hours spent studying by students who sit in the front of the classroom is greater than that of students who sit in the back of the classroom." Dozens of randomly selected students were asked how many hours they study per week. There were 35 students who said that they tend to sit toward the front of the classroom, and their reported number of study hours per week had a mean of 17.26 and standard deviation of 9.34. There were 36 students who said they tend to sit toward the back of the classroom, and they had a mean of 11.08 and standard deviation of 8.64. The standard deviation for the population of students who sit in the front is assumed to be the same as that for those who sit in the back. Test the claim at the 0.01 significance level. a. 2.895 b. 2.892 c. 10.933 d. 13.281
Solution
Step 1 ：We are given the following values: the number of students who sit in the front of the class (\(n1\)) is 35, their mean study hours per week (\(\bar{x1}\)) is 17.26, and their standard deviation (\(s1\)) is 9.34. The number of students who sit in the back of the class (\(n2\)) is 36, their mean study hours per week (\(\bar{x2}\)) is 11.08, and their standard deviation (\(s2\)) is 8.64.
Step 2 ：We are testing the claim that the average weekly number of hours spent studying by students who sit in the front of the classroom is greater than that of students who sit in the back of the classroom. This is a two-sample t-test.
Step 3 ：The test statistic for a two-sample t-test is calculated using the formula: \(t = \frac{(\bar{x1} - \bar{x2}) - 0}{\sqrt{(s1^2/n1) + (s2^2/n2)}}\)
Step 4 ：Substituting the given values into the formula, we get: \(t = \frac{(17.26 - 11.08) - 0}{\sqrt{(9.34^2/35) + (8.64^2/36)}}\)
Step 5 ：Solving the above expression, we find that the test statistic \(t\) is approximately 2.892
Step 6 ：Final Answer: The value of the test statistic used in the hypothesis test is \(\boxed{2.892}\)
