Confidence intervals for a mean Quiz

1. A normal population has $\sigma=10$. A sample of $25$ has mean $80$. What is the $95\%$ interval?

• A. $(76.08,\ 83.92)$
• B. $(60.4,\ 99.6)$
• C. $(78.04,\ 81.96)$
• D. $(77.5,\ 82.5)$

2. Which gives the narrowest interval, other things equal?

• A. $99\%$ level, $n=20$
• B. $95\%$ level, $n=20$
• C. $90\%$ level, $n=80$
• D. $99\%$ level, $n=80$

3. A $95\%$ interval for a mean is $(12.1,\ 14.5)$. A manufacturer claims the mean is $15$. What follows?

• A. The claim is certainly false
• B. The claim is consistent with the data
• C. There is evidence at the $5\%$ level that the mean is below $15$
• D. The mean is $13.3$ with probability $0.95$

4. A large sample has $n=100$, $\bar x=50$ and $s^2=64$. Find the $99\%$ interval.

• A. $(48.43,\ 51.57)$
• B. $(47.94,\ 52.06)$
• C. $(33.4,\ 66.6)$
• D. $(49.2,\ 50.8)$

5. From a sample of $n=40$, $\sum x=1200$ and $\sum x^2=37\,000$. What is the unbiased estimate of the variance?

• A. $25$
• B. $24.4$
• C. $25.6$
• D. $1000$