Question

the mean exam score for 43 male high school students is 21.5 and the population standard deviation is 4.9. the mean exam score for 52 female high school students is 20.1 and the population standard deviation is 4.1. at α = 0.01, can you reject the claim that male and female high school students have equal exam scores? complete parts (a) through (e).
click here to view page 1 of the standard normal distribution table.
click here to view page 2 of the standard normal distribution table.

○ g. z < 1.64 ○ h. z < -2.33, z > -2.33
(c) find the standardized test statistic z for μ₁ - μ₂.
z = 1.49 (rounded to two decimal places as needed.)
(d) decide whether to reject or fail to reject the null hypothesis. choose the correct answer below.
○ a. reject h₀. the standardized test statistic is in the rejection region.
○ b. fail to reject h₀. the standardized test statistic is not in the rejection region.
○ c. reject h₀. the standardized test statistic is not in the rejection region.
○ d. fail to reject h₀. the standardized test statistic is in the rejection region.
(e) interpret the decision in the context of the original claim.
at the □% significance level, there is □ evidence to □ the claim that male high school students have exam scores □ female high school students exam scores.

Explanation:

For part (e), the significance level is 0.01 (1%). Since we failed to reject \( H_0 \), there is not enough evidence to reject the claim that male and female scores are equal. So:

• Significance level: 1% (from \( \alpha = 0.01 \)).
• Evidence: "not enough" (as we failed to reject \( H_0 \)).
• Action: "reject" is incorrect; we "fail to reject" the claim (or "reject" the alternative, but contextually, the claim is equality, so we don't have evidence to reject it, meaning we can't say they differ).
• Relationship: "equal to" (since the claim is they have equal scores).

Answer:

At the \(\boldsymbol{1}\%\) significance level, there is \(\boldsymbol{\text{not enough}}\) evidence to \(\boldsymbol{\text{reject}}\) the claim that male high school students have exam scores \(\boldsymbol{\text{equal to}}\) female high school students' exam scores.