Tests for the difference between two Normal means Quiz

1. Independent samples: $n_x=25$, $\sigma_x=5$; $n_y=25$, $\sigma_y=5$. The standard error of $\bar X-\bar Y$ is

• A. $\sqrt2$
• B. $2$
• C. $1$
• D. $\sqrt{50}$

2. A two-tailed test gives $z=2.10$. At the $5\%$ level

• A. $H_0$ is not rejected
• B. $H_0$ is rejected because $2.10>1.96$
• C. $H_0$ is rejected because $2.10>1.645$ only
• D. no conclusion can be made

3. Which is the correct alternative hypothesis for 'the mean of $X$ is smaller than the mean of $Y$'?

• A. $\mu_x>\mu_y$
• B. $\mu_x\ne\mu_y$
• C. $\bar x<\bar y$
• D. $\mu_x<\mu_y$

4. Why may sample variances replace population variances in the test statistic?

• A. The samples are large, so by the Central Limit Theorem $\bar X-\bar Y$ is approximately Normal and $s^2$ is a good estimate
• B. The population variances are always equal
• C. The samples are small
• D. $s^2$ is always larger than $\sigma^2$

5. A two-tailed test has tail probability $0.032$ beyond the test statistic. The $p$-value is

• A. $0.016$
• B. $0.968$
• C. $0.064$
• D. $0.032$