# Can someone please check my answers? It's over confidence intervals

#### SpaceElephant

##### New Member
This isn't techinally homework. It's extra practice questions giving by my teacher. I just want to make sure I'm understanding everything correctly. If I have a question wrong, can you please give me the right answer and explain it in great detail?

1. Construct a 95 percent confidence interval on the population mean if a sample of 51 items had an average of 23.2 inches
Answer: (25.4, 58.8)

2. Construct a 90 percent confidence interval on the population mean if a sample of 51 items had an average of 23.2 inches.
Answer: This cannot be determined without knowing the standard deviation of the population, or at least the standard deviation of the sample.

3. Construct a 99 percent confidence interval on the population standard deviation if a sample of 51 items had a standard deviation of 23.2
Answer: 19.41 < σ < 28.84

4. A sample of 1200 voters indicated that 820 were in favor of proposition A. Construct a 95 percent confidence interval on the proportion of the population who supports proposition A.
Answer: (0.657, 0.709)

5. A sample of 1200 voters indicated that 820 were in favor of proposition A. Construct a 99 percent confidence interval on the proportion of the population who supports proposition A.
Answer: (0.648, 0.718)

6. What sample size is needed to estimate at the 90 percent confidence level the proportion of Sandburg students who were flipflops to class on a regular basis, with an error of the estimate of 3 percent?
Answer: 751.67

7. A politician wants to estimate the percentage of her constituents who support banning Facebook from the planet. In order to be 90 percent confident with a margin of error 2.5 percent, what sample size is needed?
Answer: 1082.41

8. Construct a 100 percent confidence interval on the population mean if a sample of 51 items had an average of 23.2 inches.
Answer: (16.30, 30.1)

9. A sample of 61 items had a low value of 123 and a high value of 321. Using the range rule of thumb to estimate the sample standard deviation, construct a 99 percent confidence interval on the population variance.
Answer: 0.76 < σ² < 1.689

10. Past experience indicates that the proportion of the population who supports term limits on Illinois governors is 35 percent. What sample size is needed to estimate the proportion with 95 percent confidence of the population who supports term limits on Illinois governors with a margin of error of 5 percent?
Answer: 350

11. Past experience indicates that the proportion of the population who supports term limits on Illinois governors is unknown. What sample size is needed to estimate the proportion with 95 percent confidence of the population who supports term limits on Illinois governors with a margin of error of 5 percent?
Answer: 271

12. Why are the answers to problem 10 and 11 different?
Answer: Different confidence levels, so different critical values?