Exercise · ZW-P-VALUE-006 · ★★☆ Intermediate
We test \(H_0:\mu=50\) against \(H_1:\mu>50\) with \(n=36\), \(\bar x=53\) and \(\sigma=12\). What is the p-value?
Choose one option.
Show answer
- A. \(0.0668\)
Explanation
First \(z=(53-50)/2=1.5\); then \(p=1-\Phi(1.5)=0.0668\) (right tail only).
Review the concept: p-value
The \(p\)-value is the probability \(P\), computed assuming the null hypothesis \(H_0\) is true, of obtaining a result at least as extreme as the one observed.
\[p=P\big(\text{result at least as extreme}\mid H_0\big)\]
More practice problems: p-value
- ZW-P-VALUE-001 Two-sided test with z=1.5. What is the p-value?
- ZW-P-VALUE-002 Right-tailed test with z=2.0. What is the p-value?
- ZW-P-VALUE-003 A p-value of 0.03 and α=0.05. What is decided?
- ZW-P-VALUE-004 A p-value of 0.03 and α=0.01. What is decided?
- ZW-P-VALUE-005 Two-sided test with z=-2.4. What is the p-value?
- ZW-P-VALUE-007 We get p=0.04. Which interpretation is correct?
- ZW-P-VALUE-008 Two-sided test with z=1.96. What is the approximate p-value?
- ZW-P-VALUE-009 If H_0 is true and the statistic is continuous, what is the probability that p≤0.05?