Hypothesis tests for a mean Quiz

1. $\sigma=4$, $n=64$, $H_0:\mu=50$ and $\bar x=51.2$. What is the test statistic?

• A. $2.4$
• B. $0.3$
• C. $19.2$
• D. $0.15$

2. What is the critical value for a one-tailed test, upper tail, at the $1\%$ significance level?

• A. $1.645$
• B. $1.96$
• C. $2.576$
• D. $2.326$

3. A two-tailed $5\%$ test of $H_0:\mu=100$ has $\sigma=5$ and $n=25$. Which is the critical region for $\bar X$?

• A. $\bar X<95.1$ or $\bar X>104.9$
• B. $\bar X<99.02$ or $\bar X>100.98$
• C. $\bar X<98.04$ or $\bar X>101.96$
• D. $\bar X<98.355$ or $\bar X>101.645$

4. A population is skewed, $\sigma$ is known and $n=60$. Why can a Normal-based test for $\mu$ be used?

• A. The population is Normal
• B. By the Central Limit Theorem, as $n$ is large
• C. Because $\sigma$ is known
• D. Because $\bar x$ is unbiased

5. In a lower-tail test, $z=-1.75$ (so $p=0.040$). What is the correct conclusion?

• A. Reject $H_0$ at $5\%$ and at $1\%$
• B. Reject $H_0$ at $5\%$ but not at $1\%$
• C. Do not reject at $5\%$ but reject at $1\%$
• D. Do not reject $H_0$ at either level