Question

question 1 of 6, step 1 of 3
an sat prep course claims to increase student scores by more than 60 points, on average. to test this claim, 9 students who have previously taken the sat are randomly chosen to take the prep course. their sat scores before and after completing the prep course are listed in the following table. test the claim at the 0.01 level of significance assuming that the population distribution of the paired differences is approximately normal. let ( d = (\text{scores after completing the prep course}) - (\text{scores before completing the prep course}) ).

sat scores
after prep course	1600	1520	1550	1220	1310	1220	1230	1450	1250

step 1 of 3: state the null and alternative hypotheses for the test. fill in the blank below.
( h_0: mu_d = 60 )
( h_a: mu_d _____ 60 )

answer
options: (
eq ), ( < ), ( > )

Explanation:

Step1: Understand the Claim

The prep course claims to increase scores by more than 60 points on average. So we test if the mean difference \( \mu_d \) (after - before) is greater than 60.

Step2: Formulate Hypotheses

• Null hypothesis \( H_0 \): \( \mu_d = 60 \) (no more than 60 - point increase, or exactly 60).
• Alternative hypothesis \( H_a \): \( \mu_d > 60 \) (supports the claim of more than 60 - point increase).

Answer:

\( > \) (So the correct symbol for \( H_a: \mu_d \) ______ 60 is \( > \), corresponding to the option with \( > \).)