In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. What is an appropriate test value for a z test?
A) 0.29
B) 8.35
C) 2.40
D) 1.23

Question

In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. What is an appropriate test value for a z test? 
A) 0.29 
B) 8.35 
C) 2.40 
D) 1.23

Quizplus · Accepted Answer

Since we are comparing two groups (freshmen and seniors), the appropriate test is a two-sample z-test. The test value for a two-sample z-test is:

z = (x̄1 - x̄2) / (σ(sqrt(1/n1 + 1/n2)))

where x̄1 and x̄2 are the sample means, n1 and n2 are the sample sizes, and σ is the common population standard deviation (which we don't know, so we will use the sample standard deviations instead).

Since we don't have any specific values for the means or standard deviations, we cannot calculate the exact test value. However, we can use the fact that the test value for a two-sample z-test follows a standard normal distribution (with mean 0 and standard deviation 1) under the null hypothesis of equal means. Therefore, we can use a standard normal table or calculator to find the appropriate test value.

For a two-sided test at the 5% significance level (which is the most commonly used standard), the critical values are ±1.96. Therefore, the appropriate test value for a z-test is z = ±1.96.

Note that none of the answer choices match exactly with this value. However, C is the closest one (2.40), so it is the best choice.

In October, the Campus Bookstore Asked a Random Set of Freshmen