Hypothesis tests for the difference between two means Quiz

1. $\sigma_x=3$, $n_x=9$, $\sigma_y=4$, $n_y=16$. What is the variance of $\bar X-\bar Y$?

• A. $0$
• B. $2$
• C. $7$
• D. $1.41$

2. $\bar x=10.4$, $\bar y=9.6$ and the variance of $\bar X-\bar Y$ is $0.16$. What is the test statistic under $H_0:\mu_x=\mu_y$?

• A. $5$
• B. $0.2$
• C. $0.8$
• D. $2$

3. What is the critical value for $H_1:\mu_x<\mu_y$ at the $5\%$ level?

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

4. When may sample variances replace the population variances in a test for two means?

• A. Both samples are large
• B. Either sample is small
• C. The populations are discrete
• D. The sample means are equal

5. In a two-tailed test at $5\%$, $z=-1.4$. What is the conclusion?

• A. Reject $H_0$
• B. Do not reject $H_0$
• C. Accept $H_1$
• D. Reject $H_0$ at $1\%$ only