Advanced Placement (AP) High School

A school administrator believes that, in his school, the GPA of
seniors in their second semester is less than the GPA of seniors in
their first semester. The class size is large, so a census is not
practical because of time constraints. To test his belief, he selects a
SRS of senior GPA's from the first semester (n1 - 50) and an
independent SRS of senior GPA's from the second semester (n2-
50). He finds that x1 bar-3.1 and s1-0.8, and x2 bar.-2.8 and $2
-0.5. He defines p1 as the average GPA of seniors in semester 1
and u2 as the average GPA of seniors in semester 2.
The test of his belief for
statistical significance will be
a:
A. two-tailed test.
B. one-tailed left test.
C. one-tailed right test.

Answers

Answer 1

The test of his belief for statistical significance will be a: one-tailed right test. The correct option is C.

We can conduct a hypothesis test to verify the administrator's assertion that seniors' second-semester GPAs are lower than seniors' first-semester GPAs.

According to the null hypothesis (H0), there is no discernible difference between the two means.

H0: u1 - u2 = 0

The contrary hypothesis (Ha) would assert that the second semester's GPA is, in fact, lower than the first semester's GPA:

Ha: u1 - u2 > 0

We are using a one-tailed right test because the administrator thinks the second semester's GPA is lower.

We are eager in finding out if there is evidence to support the alternative hypothesis that the second semester's GPA is lower.

Therefore, C. One-tailed Right Test is the appropriate response.

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