2. Suppose the 95% confidence interval estimate of the population proportion p is 0.405

(a) There is a 95% chance that the true value of p will fall between 0.405 and 0.455.

(b) 95% of sample proportions will fall between 0.405 and 0.455.

(c) We are 95% confident that the interval from 0.405 to 0.455 actually does contain the true value of the population proportion, p.

(d) All of them are correct.

(e) None of the above.

3. Which of the following is not a characteristic of Students' t-distribution?

(a) It is a symmetric distribution.

(b) For large samples, the t and z distributions are nearly equivalent.

(c) It depends on degrees of freedom.

(d) It has mean of 0 and standard deviation of 1.

(e) None of the above

4. Suppose the confidence interval for a population proportion is (0.58, 0.81). Find the sample proportion, p and the margin of error, E.

5. A private opinion poll is conducted for a politician to determine what proportion of the population favors adding more national parks. How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%?

6. Find the critical value z a/2 corresponding to a

(a) 92% confidence level.

(b) 95% confidence level.

(c) 99% confidence level.

7. Determine the point estimate of the population proportion, the margin of error and the number of individuals in the sample with the specified characteristics, x, for the sample size provided.

(a) Lower bound: 0.051, upper bound: 0.074, n=1120

(b) Lower bound: 0.853, upper bound: 0.871, n=1680

8. Construct a confidence interval of the population proportion at the given level of confidence.

(a) x=30, n=150, 90% confidence.

(b) x=400, n=1200, 95% confidence.

9. In a USA Today poll, 768 of 1024 randomly selected adult Americans aged 18 or older stated that a candidate's positions on the issue of family values are extremely or very important in determining their vote for president.

(a) Verify that the requirements for constructing a confidence interval for p are satisfied.

(b) Construct a 99% confidence interval for the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president.

10. A Gallup poll of 1487 adults showed that 43% of the respondents have Facebook pages.

(a) Find the margin of error E that corresponds to a 95% confidence level.

(b) Find the 95% confidence interval estimate of the population proportion p.

(c) Based on the results, can we safely conclude that fewer than 50% of adults have Facebook pages?

11. Suppose a 90% confidence interval for turns out to be (1000, 2100). If this interval was based on a sample of size n=25 explain what assumptions are necessary for this interval to be valid.

(a) The sampling distribution must be biased with 24 degrees of freedom.

(b) The population must have an approximately normal distribution.

(c) The sampling distribution of the sample mean must have a normal distribution.

(d) None of the above.

12. Determine the critical value Z a/2 that corresponds to the given level of confidence.

(a) 90%

(b) 99%

(c) 92%

(d) 80%

13. Compute (a) t0.25; df=15 (b) t0.20; df=26 (c) t0.05; df=30

14. Use Calculator to compute t a/2 for (a) a=0.10 ; df=15 (b) a=0.15 ; df=25 (c) a=0.25 ; df=30

15. Construct a 90% confidence interval for the population mean, . Assume the population has a normal distribution. A sample of 15 randomly selected math majors has a grade point average of 2.86 with a standard deviation of 0.78. Round to the nearest hundredth.

16. A simple random sample of size n is drawn. The sample mean, x, is found to be 35,and the sample standard deviation s, is found to be 8.5.

(a) Construct a 90% confidence interval for the population mean, if the sample size, n, is. 40.

(b) Construct a 98% confidence interval for the population mean, if the sample size, n, is. 65.

(c) Construct a 95% confidence interval for the population mean, if the sample size, n, is. 18. What condition must be satisfied to compute the confidence interval?

17. Based on a survey of 140 employed persons in a city, the mean and standard deviation of the commuting distances between home and the principal place of business are found to be 8.6 and 4.3 miles, respectively. Determine a 90% confidence interval for the mean commuting distance for the population of all employed persons in the city.

18. Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean (population mean) with 98% confidence. Assume that s=14 based on earlier studies.

19. Construct a 95% confidence interval for the population standard deviation s of a random sample of 15 adult men who have a mean weight of 165.2 pounds and a standard deviation of 14.5 pounds. Assume the population is normally distributed.

20. You are the operations manager for American Airlines and you are considering a higher fare level for passengers in aisle seats. You want to estimate the percentage (proportion) of passengers who now prefers aisle seats. Assume that you want to be 99% confident that the sample percentage is within 2.5 percent of the true proportion percentage. How many randomly selected air passengers must you survey?

(a) Assume that nothing is known about the percentage of passengers who prefer aisle seats.

(b) Assume that a prior survey suggests that about 38% of air passengers prefer an aisle seat.