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. z > -3.08 b. z < -1.64, z > 1.64 c. z > 2.58 d. z < -2.58, z > 2.58 e. z < -2.33 f. z < -3.08, z > -3.08 g. z < 1.64 h. z < -2.33, z > -2.33 (c) find the standardized test statistic z for μ₁ - μ₂. z = 1.49 (round 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.

Explanation:

Step1: Identify Rejection Region

The significance level \(\alpha = 0.01\) for a two - tailed test (since we are testing if male and female scores are equal, so the alternative hypothesis is two - tailed). For a two - tailed test with \(\alpha=0.01\), the critical \(z\) - values are \(z = \pm2.58\) (from standard normal distribution table). The rejection region is \(z < - 2.58\) or \(z>2.58\).

Step2: Compare Test Statistic with Rejection Region

The standardized test statistic \(z = 1.49\). We check if \(1.49\) lies in the rejection region (\(z < - 2.58\) or \(z>2.58\)). Since \(- 2.58<1.49<2.58\), the test statistic is not in the rejection region.

Step3: Make a Decision about \(H_0\)

If the test statistic is not in the rejection region, we fail to reject the null hypothesis \(H_0\) (the null hypothesis is that male and female high school students have equal exam scores).

Answer:

B. Fail to reject \(H_0\). The standardized test statistic is not in the rejection region.