Exercise · ZW-HYPOTHESIS-TEST-009 · ★★★ Advanced
With a fixed sample, what happens to \(\beta\) if \(\alpha\) rises from \(0.01\) to \(0.05\)?
Choose one option.
Show answer
- A. It falls, because the rejection region grows
Explanation
A larger rejection region makes it easier to detect a false \(H_0\), so \(\beta\) falls; the cost is more Type I errors. With fixed \(n\) the two errors trade off.
Review the concept: Hypothesis test
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
- ZW-HYPOTHESIS-TEST-001 We test H_0:μ=50 with n=36, bar x=53 and known σ=12. What is the statistic z?
- ZW-HYPOTHESIS-TEST-002 With z=1.5, a two-sided test and α=0.05 (critical value 1.96), what is the decision?
- ZW-HYPOTHESIS-TEST-003 What is a Type I error?
- ZW-HYPOTHESIS-TEST-004 What is a Type II error?
- ZW-HYPOTHESIS-TEST-005 We test H_0:μ=50 with n=25, bar x=46 and σ=10. What is z?
- ZW-HYPOTHESIS-TEST-006 For H_1:μ>μ_0 with α=0.05 we reject if z>1.645. If z=1.8, what is concluded?
- ZW-HYPOTHESIS-TEST-007 For H_1:μ<μ_0 with α=0.01 we reject if z<-2.326. If z=-2.0, what is concluded?
- ZW-HYPOTHESIS-TEST-008 We test H_0:μ=50 against H_1:μne50 with n=64, bar x=47.6, σ=8 and α=0.05. What is concluded?