Covers \( \mu_0,\mu_1 \), H₀/H₁, z vs t, p-values, and tail choice. No Type I/II questions in this quiz.
1) In a one-sample z-test with known \( \sigma \), the standard error is \( \sigma/\sqrt{n} \).
2) In a one-sample t-test, the degrees of freedom are \( n-1 \).
3) For a two-sided test at \( \alpha=0.05 \), the critical value is \( \pm 1.645 \).
4) For \( H_1:\mu>\mu_0 \), the rejection region is in the left tail.
5) A p-value is the probability that \( H_0 \) is true, given the data.
6) If \( p=0.03 \) and \( \alpha=0.05 \), you should fail to reject \( H_0 \).
7) If a 95% CI for \( \mu \) excludes \( \mu_0 \), a two-sided test at \( \alpha=0.05 \) would reject \( H_0 \).
8) As \( n \) grows large, t critical values approach the corresponding z critical values.
9) In a two-sided test, \( \mu_1 \) must equal \( \mu_0+2 \); other values are invalid.
10) When \( \sigma \) is unknown and \( n \) is small, you should still use a z-test by plugging \( s \).
11) For \( H_1:\mu<\mu_0 \) at level \( \alpha \), the rule “reject if \( \bar x > \mu_0 + z_{1-\alpha}\cdot SE \)” is correct.
12) For a two-sided test, the p-value equals \( 2 \times \) the one-sided tail area beyond \( |z| \) (or \( |t| \)).
13) \( \mu_1 \) is the same thing as the sample mean \( \bar x \).
14) “Fail to reject \( H_0 \)” proves the null hypothesis is true.
15) With the same \( \alpha \), switching from two-sided to one-sided makes rejection easier in the chosen direction.