Question

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 0.10 level of significance assuming that the population distribution of the paired differences is approximately normal. let d = (scores after completing the prep course) − (scores before completing the prep course). sat scores before prep course: 1500, 1090, 1140, 1200, 1040, 1350, 1210, 1500, 1210; after prep course: 1680, 1130, 1230, 1240, 1260, 1600, 1310, 1700, 1290 step 1 of 3: state the null and alternative hypotheses for the test. fill in the blank below. h₀: μ_d = 60 hₐ: μ_d ______ 60 answer options: <, ≠, > tables keypad keyboard shortcut

Explanation:

Step1: Understand the Claim

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

Step2: Determine Hypotheses

• Null hypothesis \( H_0 \): \( \mu_d = 60 \) (no more than 60 point increase, or exactly 60).
• Alternative hypothesis \( H_a \): Since the claim is "more than 60", we use \( \mu_d > 60 \) to test the claim.

Answer:

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