Exercise · ZW-HYPOTHESIS-TEST-005 · ★★☆ Intermediate
We test \(H_0:\mu=50\) with \(n=25\), \(\bar x=46\) and \(\sigma=10\). What is \(z\)?
Choose one option.
Show answer
- A. \(-2\)
Explanation
The standard error is \(10/5=2\) and \(z=(46-50)/2=-2\). The sign matters: the sample mean lies below \(\mu_0\).
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-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?
- ZW-HYPOTHESIS-TEST-009 With a fixed sample, what happens to β if α rises from 0.01 to 0.05?