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. a. male and female high school students have different exam scores. b. male and female high school students have equal exam scores. c. male high school students have greater exam scores than female students. d. male high school students have lower exam scores than female students. what are h₀ and hₐ? a. h₀: μ₁ ≥ μ₂, hₐ: μ₁ < μ₂; b. h₀: μ₁ = μ₂, hₐ: μ₁ ≠ μ₂; c. h₀: μ₁ ≤ μ₂, hₐ: μ₁ > μ₂; d. h₀: μ₁ ≠ μ₂, hₐ: μ₁ = μ₂; e. h₀: μ₁ > μ₂, hₐ: μ₁ ≤ μ₂; f. h₀: μ₁ < μ₂, hₐ: μ₁ ≥ μ₂ (b) find the critical value(s) and identify the rejection region(s). the critical value(s) is/are. (round to two decimal places as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Identify Test Type

This is a two - tailed z - test (since population standard deviations are known) with \(\alpha = 0.01\). For a two - tailed test, we split \(\alpha\) into two tails, so \(\alpha/2=0.005\) in each tail.

Step2: Find Critical Values

We look for the z - scores that correspond to the areas of \(0.005\) in the left tail and \(0.995\) in the left - to - right cumulative area (or \(0.005\) in the right tail). From the standard normal distribution table, the z - score for which \(P(Z < z)=0.005\) is \(z=- 2.58\) and the z - score for which \(P(Z < z)=0.995\) is \(z = 2.58\).

Answer:

The critical value(s) is/are \(-2.58, 2.58\)