Confidence intervals from small samples Quiz

1. For $\nu=9$ the $2.5\%$ critical value is $2.262$. A sample of $10$ has $\bar x=50$ and $s=3$. Find the $95\%$ interval.

• A. $(47.85,\ 52.15)$
• B. $(48.14,\ 51.86)$
• C. $(43.21,\ 56.79)$
• D. $(49.05,\ 50.95)$

2. Why is a $t$ interval wider than a $z$ interval from the same $\bar x$, $s$ and $n$?

• A. $s$ is larger in the $t$ interval
• B. The $t$ critical value is larger because of the heavier tails
• C. $n$ is smaller in the $t$ interval
• D. The sample mean is different

3. A sample has $n=20$. How many degrees of freedom are used?

• A. $20$
• B. $21$
• C. $18$
• D. $19$

4. A $99\%$ interval and a $95\%$ interval are calculated from the same sample. Which statement is true?

• A. The $99\%$ interval is narrower
• B. They have the same width
• C. The $99\%$ interval is wider because its critical value is larger
• D. The $99\%$ interval is narrower because the standard error is smaller

5. A $95\%$ interval for a mean is $(12.4,\ 15.2)$. A claim is that the mean is $16$. What follows?

• A. Evidence at the $5\%$ level that the mean is below $16$
• B. The claim is consistent with the data
• C. The claim is proved false
• D. The mean is $13.8$ exactly