Suppose John wants to open a learning center for high school students in his com

Question

Suppose John wants to open a learning center for high school students in his community. John wants to compare the average time area high school students spend studying per week with the regional average, 17.4 h.

John surveys 15 randomly selected local high school students, asking how much time they spend studying in a typical week. Although he does not know the standard deviation of the underlying population, he is confident that the population is normally distributed because other studies indicate that study times are normally distributed, and graphs of his sample data indicate normality.

Choose the correct test procedure that John should use to test if the mean weekly study time from his sample differs from 17.4 h.

A) one-sample, right-tailed t-test for a mean

B) one-sample, two-tailed z-test for a mean

C) one-sample, left-tailed t-test for a mean

D) one-sample, two-tailed t-test for a mean

E) one-sample, right-tailed z-test for a mean

Explanation / Answer

Correct Answer:

D) one-sample, two-tailed t-test for a mean

Explanation:

The null and alternative hypotheses for the given scenario are summarized as below:

Null hypothesis: H0: The mean weekly study time is 17.4 hours.

Alternative hypothesis: Ha: The mean weekly study time is different from 17.4 hours.

H0: µ = 17.4 versus Ha: µ 17.4

Alternative hypothesis contains ‘not equal to’ which indicate a two tailed test.

Population standard deviation is not given, which indicate a t test.

This means, we require a one sample two tailed t-test for the given scenario.

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