Question

obstacle course times an obstacle course was set up on a campus, and 9 volunteers were given a chance to complete it while they were being timed. they then sampled a new energy drink and were given the opportunity to run the course again. the \before\ and \after\ times in seconds are shown below. is there sufficient evidence at α=0.05 to conclude that the students did better the second time? assume the variables are normally distributed.
student | before | after
--- | --- | ---
1 | 82 | 78
2 | 69 | 65
3 | 68 | 70
4 | 75 | 68
5 | 76 | 73
6 | 81 | 76
7 | 77 | 73
8 | 77 | 68
9 | 72 | 70
(a) state the hypotheses and identify the claim.
h₀ :
h₁ :
this hypothesis test is a one - tailed test.

Explanation:

Step1: Define Hypotheses

We want to test if students did better the second time, meaning the "after" times (let \( \mu_d \) be the mean of the differences \( d = \text{Before} - \text{After} \)) are such that \( \mu_d > 0 \) (since a smaller "after" time means better performance, so \( \text{Before} - \text{After} > 0 \) would mean after is better).

• Null Hypothesis (\( H_0 \)): \( \mu_d \leq 0 \) (students did not do better the second time, or did worse/ same)
• Alternative Hypothesis (\( H_1 \)): \( \mu_d > 0 \) (students did better the second time, this is the claim)

Step2: Identify Claim

The claim is that students did better the second time, which corresponds to \( H_1: \mu_d > 0 \). The null hypothesis is the complement, \( H_0: \mu_d \leq 0 \).

Answer:

\( H_0: \mu_d \leq 0 \) (not claim), \( H_1: \mu_d > 0 \) (claim)