Confidence intervals for a Normal mean Quiz

1. $\sigma=12$, $n=36$, $\bar x=80$. What is the $95\%$ confidence interval for $\mu$?

• A. $(56.5,\ 103.5)$
• B. $(78,\ 82)$
• C. $(79.7,\ 80.3)$
• D. $(76.1,\ 83.9)$

2. A $99\%$ confidence interval is calculated from the same sample as a $95\%$ interval. The $99\%$ interval is:

• A. Narrower
• B. The same width
• C. Wider
• D. Wider only if $n$ is small

3. A $95\%$ interval for $\mu$ is $(18.4,\ 21.6)$. What is the sample mean?

• A. $20$
• B. $1.6$
• C. $3.2$
• D. $40$

4. A $95\%$ confidence interval for $\mu$ is $(18.4,\ 21.6)$. What follows for a two-tailed test of $H_0:\mu=22$ at the $5\%$ level?

• A. Do not reject $H_0$, as $22$ is outside the interval
• B. Reject $H_0$, as $22$ is outside the interval
• C. Reject $H_0$, as $22$ is inside the interval
• D. The test cannot be carried out

5. $\sigma=6$. What is the smallest $n$ for a $95\%$ interval of width at most $3$?

• A. $61$
• B. $62$
• C. $16$
• D. $8$