Question

a study was done on proctored and nonproctored tests. the results are shown in the table. assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. use a 0.01 significance level to test the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. what are the null and alternative hypotheses? oa. ( h_{0}: mu_{1}=mu_{2} ) ( h_{1}: mu_{1}>mu_{2} ) ob. ( h_{0}: mu_{1}
eq mu_{2} ) ( h_{1}: mu_{1}<mu_{2} ) oc. ( h_{0}: mu_{1}=mu_{2} ) ( h_{1}: mu_{1}<mu_{2} ) od. ( h_{0}: mu_{1}=mu_{2} ) ( h_{1}: mu_{1}
eq mu_{2} )

Explanation:

To test the claim that students taking non - proctored tests get a higher mean score than those taking proctored tests, we need to set up the null and alternative hypotheses. The null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_1\) is the claim we are testing. Since we want to test if \(\mu_2>\mu_1\) (non - proctored mean \(\mu_2\) is greater than proctored mean \(\mu_1\)), we can rewrite it as \(\mu_1<\mu_2\). The null hypothesis for a two - sample t - test (when variances are not assumed equal) is \(H_0:\mu_1 = \mu_2\).

Answer:

C. \(H_0:\mu_1=\mu_2\), \(H_1:\mu_1 < \mu_2\)