Exercise · ZW-HYPOTHESIS-TEST-007 · ★★☆ Intermediate
For \(H_1:\mu<\mu_0\) with \(\alpha=0.01\) we reject if \(z<-2.326\). If \(z=-2.0\), what is concluded?
Choose one option.
Show answer
- C. Do not reject \(H_0\)
Explanation
We need \(z<-2.326\) and \(-2.0\) does not satisfy it; at such a strict level the evidence is not enough.
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-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?
- ZW-HYPOTHESIS-TEST-009 With a fixed sample, what happens to β if α rises from 0.01 to 0.05?