Hypothesis test for the mean of a Normal distribution Quiz

1. $X\sim N(\mu,8^2)$. A sample of $16$ has mean $102$. The standard error of $\bar X$ is

• A. $8$
• B. $0.5$
• C. $2$
• D. $4$

2. Which is a correct pair of hypotheses for testing whether the mean has increased from $75$?

• A. $H_0:\mu=75$, $H_1:\mu>75$
• B. $H_0:\bar x=75$, $H_1:\bar x>75$
• C. $H_0:\mu>75$, $H_1:\mu=75$
• D. $H_0:\mu=75$, $H_1:\mu\ne75$

3. A one-tailed test at the $5\%$ level gives $p=0.03$. The correct decision is

• A. Do not reject $H_0$
• B. Reject $H_0$
• C. Accept $H_0$ as proved
• D. The test is invalid

4. In a two-tailed test at the $5\%$ level, the critical values of $z$ are

• A. $\pm1.645$
• B. $\pm2.326$
• C. $\pm1.96$
• D. $\pm2.576$

5. The same sample mean is found with a larger sample. The $p$-value will generally

• A. Get smaller
• B. Get larger
• C. Stay the same
• D. Be negative