Confidence intervals for a Normal mean Quiz

1. $\sigma=8$, $n=16$, $\bar x=50$. The $95\%$ confidence interval for $\mu$ is

• A. $(46.08,\ 53.92)$
• B. $(34.32,\ 65.68)$
• C. $(48.0,\ 52.0)$
• D. $(46.71,\ 53.29)$

2. Which statement is correct for a given sample?

• A. A $99\%$ interval is narrower than a $95\%$ interval
• B. A $99\%$ interval is wider than a $95\%$ interval
• C. Both have the same width
• D. The width depends only on $\bar x$

3. A $95\%$ confidence interval for $\mu$ is $(8.2,\ 9.6)$. A two-tailed $5\%$ test of $H_0:\mu=9.9$ would

• A. not reject $H_0$
• B. reject $H_0$ because $9.9$ is outside the interval
• C. reject $H_0$ because $9.9$ is close to $9.6$
• D. be impossible without the data

4. The $95\%$ interval width is to be at most $4$ with $\sigma=5$. Which sample size is the smallest that works?

• A. $24$
• B. $26$
• C. $7$
• D. $25$

5. The sample size is multiplied by $9$ with everything else unchanged. The width of the interval is

• A. multiplied by $9$
• B. divided by $9$
• C. divided by $3$
• D. unchanged