4.16 Confidence intervals Quiz

1. A $95\%$ interval for $\mu$ is $(12.4,\ 15.6)$. What is the sample mean?

• A. $14.0$
• B. $3.2$
• C. $1.6$
• D. $28.0$

2. Population normal, $\sigma=8$ known, $n=16$, $\bar{x}=50$. Find the margin of error for a $95\%$ interval (3 s.f.).

• A. $1.96$
• B. $3.92$
• C. $7.84$
• D. $15.7$

3. Which condition means you must use a $t$-interval?

• A. The sample is small.
• B. The population is not normal.
• C. The population standard deviation is known.
• D. The population standard deviation is unknown.

4. The confidence level is raised from $90\%$ to $99\%$ with the same data. What happens to the interval?

• A. It gets narrower.
• B. It gets wider.
• C. It is unchanged.
• D. Its midpoint moves.

5. The same $\sigma$ is used in both cases. By what factor must $n$ increase to halve the width of the interval?

• A. $2$
• B. $3$
• C. $4$
• D. $8$