Exercise · ZW-HYPOTHESIS-TEST-008 · ★★☆ Intermediate
We test \(H_0:\mu=50\) against \(H_1:\mu\ne50\) with \(n=64\), \(\bar x=47.6\), \(\sigma=8\) and \(\alpha=0.05\). What is concluded?
Choose one option.
A Do not reject \(H_0\), since \(z=2.4\) is positive B Do not reject \(H_0\), since \(z=-0.3\) C Reject \(H_0\), since \(z=-19.2\) D Reject \(H_0\), since \(z=-2.4\) and \(|z|>1.96\) Show answer D. Reject \(H_0\), since \(z=-2.4\) and \(|z|>1.96\)← Back to the question
Explanation The standard error is \(8/8=1\) and \(z=-2.4\). Since \(|z|=2.4>1.96\), \(H_0\) is rejected.
A hypothesis test is a rule that, from sample data, decides whether to reject the null hypothesis \(H_0\), which fixes a value \(\theta_0\) for a parameter \(\theta\), in favor of the alternative \(H_1\).
\[H_0:\theta=\theta_0\quad\text{versus}\quad H_1:\theta\ne\theta_0\]
More practice problems: hypothesis test