# Sample Size & Confidence Interval

1. The library New York City Public Library asked assistant interval estimate number books checked day. The assistant a sample found 880 books. The librarian interval estimate 790 970 books checked day. Which efficient unbiased point estimate number books checked day New York City Public Library is?

2. A researcher dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200.

a. What is the sample size that should be used?

b. What sample size should be used if using a 95% confidence level?

c. What sample size should be used if using a 90% confidence level (to estimate a population mean within 40 units given that the population standard deviation is 200)?

3. Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.

a. What is the 95% confidence interval estimate of the population mean?

b. Wha tis the 99% confidence interval estimate of the population mean?

c. What is the 90% confidence interval estimate of the population mean?

d. What is the 95% confidence interval estimate of the population mean if the sample size is changed 300 while the sample mean remains at 6.5 hours?

e. What is the 95% confidence interval estimate of the population mean if the sample size is 100 while the sample mean is changed to 5.0 hours?

f. What is the 95% confidence interval of the population mean if the sample size is 100, the sample mean is 6.5 hours, while the population standard deviation is changed to 2.0 hours?

4. The p-value of a test is the:

Smallest ? at which the null hypothesis can be rejected.

Largest ? at which the null hypothesis can be rejected.

Smallest ? at which the null hypothesis cannot be rejected.

Largest ? at which the null hypothesis cannot be rejected.

5. In order to determine the p-value, which of the following is not needed?

a. The level of significance. c. The value of the test statistics.

b. The value of the test statistics. d. All of these choices are needed.

6. A Type I error occurs when we:

a. Reject a false null hypothesis. c. Reject a true null hypothesis.

b. Don't reject a false null hypothesis. d. Don't reject a true null hypothesis.

7. A Type II error occurs when we:

a. Reject a false null hypothesis. c. Reject a true null hypothesis

b. Don't reject a false null hypothesis. d. Don't reject a true null hypothesis.

8. In a criminal trial, a Type I error is made when :

a. A guilty defendant is acquitted. c. An innocent person is convicted.

b. A guilty defendant is convicted. d. An innocent person is acquitted.

9. In a criminal trial a Type II error is made when:

a. A guilty defendant is acquitted. c. An innocent person is convicted.

b. A guilty defendant is convicted. d. An innocent person is acquitted.

10. A researcher wants to study the average miles run per day for marathon runners. In testing the hypotheses: H?: µ=25 miles vs. H?: µ?25 miles, random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10, produced a mean of 22.8 miles weekly.

a. What is the test statistic (z)?

b. What is the rejection region associated with 5% significance level?

c. What is the p-value?

d. What can we conclude at the 5% significance level regarding the null hypothesis?

e. What is the 95% confidence interval estimate of the population mean?

#### Solution Summary

Sample size and confidence intervals are provided.