Question

the mean exam score for 45 male high school students is 24.1 and the population standard deviation is 4.5. the mean exam score for 52 female high school students is 21.1 and the population standard deviation is 4.2. at $\alpha = 0.01$, 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. (c) find the standardized test statistic z for $\mu_1 - \mu_2$. $z = 3.37$ (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 $h_0$. the standardized test statistic is not in the rejection region. b. fail to reject $h_0$. the standardized test statistic is in the rejection region. c. fail to reject $h_0$. the standardized test statistic is not in the rejection region. d. reject $h_0$. 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:

Step1: Recall the significance level

The significance level $\alpha = 0.01$ for a two - tailed test. The critical values are $z=\pm2.58$ (from the standard normal distribution table). The rejection region is $z < - 2.58$ or $z>2.58$.

Step2: Analyze the test statistic

The standardized test statistic $z = 3.37$. Since $3.37>2.58$, the test statistic is in the rejection region.

Answer:

At the $1\%$ significance level, there is sufficient evidence to reject the claim that male high school students have exam scores equal to female high school students' exam scores.