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) identify the claim and state h₀ and hₐ. what is the claim? 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

Explanation:

For the claim: The problem states "can you reject the claim that male and female high school students have equal exam scores", so the claim is that they have equal scores, which matches option B.

For \( H_0 \) and \( H_a \): The null hypothesis \( H_0 \) typically represents the claim being tested (equality here), so \( H_0: \mu_1 = \mu_2 \). The alternative hypothesis \( H_a \) is the opposite of the null when testing a two - tailed hypothesis (since we are testing if they are equal or not), so \( H_a: \mu_1
eq\mu_2 \), which matches option B.

Answer:

The claim: B. Male and female high school students have equal exam scores.
\( H_0 \) and \( H_a \): B. \( H_0: \mu_1 = \mu_2 \), \( H_a: \mu_1
eq\mu_2 \)