Exercise · ZW-P-VALUE-008 · ★★☆ Intermediate
Two-sided test with \(z=1.96\). What is the approximate p-value?
Choose one option.
Show answer
- D. \(0.05\)
Explanation
\(p=2\,[1-\Phi(1.96)]=2(0.025)=0.05\): that is why \(1.96\) is the critical value at the \(5\,\%\) level.
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-006 We test H_0:μ=50 against H_1:μ>50 with n=36, bar x=53 and σ=12. What is the p-value?
- ZW-P-VALUE-007 We get p=0.04. Which interpretation is correct?
- ZW-P-VALUE-009 If H_0 is true and the statistic is continuous, what is the probability that p≤0.05?