# Using the sample data from exercise 13, construct the confidence

1. Express the confidence interval -0.001<p<0.559 in the form of p-hat ± E

2. The following confidence interval is obtained for a population proportion, p: 0.883<p<0.911. Use the confidence interval limits to find the margin of error, E.

3. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 90% confidence; n=300,x=50

4. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

n=130, x=65; 90% confidence

A savings and loan association needs information concerning the checking account balances of its local customers. A

5. random sample of 14 accounts was checked and yielded a mean balance of \$664.14 and a standard deviation of \$297.29. Find a 98% confidence interval for the true mean checking account balance for local customers.

6. a. Using a t-distribution to construct a confidence interval estimate for the mean of a population and solve it.

95%; n=40; standard deviation is unknown; population appears to be skewed.

b. Suppose you make a mistake while solving the problem in part a and use the z-distribution. Solve the problem using the z-distribution.

c. Briefly discuss the reason for the difference, or the lack of difference, between the two answers

7. When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.

a. Use the traditional method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

b. Use the P-value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

c. Use the sample data to construct a 95% confidence interval estimate of the proportion of zeros. What does the confidence interval suggest about the claim that the proportion of zeros equals 0.1?

d. Compare the results from the traditional method, the P-value method, and the confidence interval method. Do they all lead to the same conclusion?

8. The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of 182.9 lb. Assuming that the standard deviation is known to be 121.8 lb, use a 0.05 significance level to test the claim that the population mean of all such bear weights is greater than 150 lb.

9. Data set 13 in appendix B lists measured voltage amounts obtained from the author’s back-up UPS (APC model CS 350). According to the manufacturer, the normal output voltage is 120 volts. The 40 measured voltage amounts from Data Set 13 have a mean of 123.59 volts and a standard deviation of 0.31 volt. Use a 0.05 significance level to test the claim that the sample is from a population with a mean equal to 120 volts.

Using the sample data from exercise 13, construct the confidence interval corresponding to the hypothesis test

10. conducted with a 0.05 significance level. What conclusion does the confidence interval suggest?

In a 1993 survey of 560 college students, 171 said that they used illegal drugs during the previous year. In a recent survey of 720 college students, 263 said that they used illegal drugs during the previous year.

11. Using the traditional method. Refer to the sample data given in exercise 17 and use a 0.05 significance level to test the claim that the mean braking distance of four-cylinder cars is greater than the mean braking distance of six-cylinder cars.

a. A simple random sample of 13 four-cylinder cars is obtained, and the braking distances are measured. The mean braking distance is 137.5 ft and the standard deviation is 5.8 ft. A simple random sample of 12 six-cylinder cars is obtained and the braking distances have a mean of 136.3 ft with a standard deviation of 9.7 ft.

b. Solve the problem in Part a, using the p-value method

12. Showing your work, including the rejection rules, and using both the traditional method and the p-value method which must lead to the same conclusion.

A simple random sample of 40 recorded speeds (in mi/h) is obtained from cars traveling on a section of highway 405 in Los Angeles. The sample has a mean of 68.4 mi/h and a standard deviation of 5.7 mi/h. Use a 0.05 significance level to test the claim that the mean speed of all cars is greater than the posted speed limit of 65 mi/h.