Hypothesis tests for a Normal mean Quiz

1. $X\sim N(80,36)$ and the sample size is $n=9$. What is the standard deviation of $\bar X$?

• A. $6$
• B. $4$
• C. $0.67$
• D. $2$

2. $H_0:\mu=50$, $\sigma=6$, $n=36$ and $\bar x=52$. Find the test statistic.

• A. $2$
• B. $0.33$
• C. $12$
• D. $0.056$

3. A test is for whether the mean of a Normal population is greater than 20. Which hypotheses?

• A. $H_0:\bar x=20,\ H_1:\bar x>20$
• B. $H_0:\mu>20,\ H_1:\mu=20$
• C. $H_0:\mu=20,\ H_1:\mu>20$
• D. $H_0:\mu=20,\ H_1:\mu<20$

4. Which statement about increasing the sample size $n$ is correct?

• A. The population standard deviation $\sigma$ decreases
• B. The standard deviation of the sample mean decreases
• C. The standard deviation of the sample mean increases
• D. The population mean $\mu$ increases

5. The critical values of $z$ for a two-tailed test at the 5% significance level are...

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