Problem
Spam: A researcher reported that $71.8 \%$ of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be $76 \%$. He examines a random sample of 500 emails received at an email server, and finds that 360 of the messages are spam. Can you conclude that the percentage of emails that are spam differs from $76 \%$ ? Use both $\alpha=0.05$ and $\alpha=0.10$ levels of significance and the $P$-value method with the table. Part: $0 / 5$ Part 1 of 5 State the appropriate null and alternate hypotheses. \[ \begin{array}{l} H_{0}: \square \\ H_{1}: \square \end{array} \] This hypothesis test is a (Choose one) $\mathbf{\nabla}$ test.
Solution
Step 1 ：The appropriate null and alternate hypotheses are: \[ \begin{array}{l} H_{0}: p = 0.76 \\ H_{1}: p \neq 0.76 \end{array} \] This hypothesis test is a two-tailed test. Explanation: The null hypothesis (H0) is the statement that the proportion of spam emails in the company is equal to 76%. The alternative hypothesis (H1) is the statement that the proportion of spam emails in the company is not equal to 76%. This is a two-tailed test because we are looking for a difference in either direction from the hypothesized proportion of 76%.
