1. A survey of 25 randomly sampled judges employed by the state of Florida found that they earned an average wage (including benefits) of $67.00 per hour. The sample standard deviation was $5.75 per hour. (Use t Distribution Table.)
a. What is the best estimate of the population mean?
b. Develop a 95% confidence interval for the population mean wage (including benefits) for these employees. (Round your answers to 2 decimal places.)
c. How large a sample is needed to assess the population mean with an allowable error of $1.00 at 98% confidence? (Round up your answer to the next whole number.)
2. An important factor in selling a residential property is the number of people who look through the home. A sample of 21 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 25 and the standard deviation of the sample was 7 people. Develop a 99% confidence interval for the population mean. (Use t Distribution Table.) (Round your answers to 2 decimal places.)
3. A population is estimated to have a standard deviation of 10. We want to estimate the population mean within 2, with a 98% level of confidence. How large a sample is required?
4. The owner of Britten’s Egg Farm wants to estimate the mean number of eggs produced per chicken. A sample of 17 chickens shows they produced an average of 18 eggs per month with a standard deviation of 7 eggs per month. (Use t Distribution Table.)
a-1. What is the value of the population mean?
It is unknown.
18
7
a-2. What is the best estimate of this value?
c. For a 99% confidence interval, what is the value of t? (Round your answer to 3 decimal places.) Develop the 99% confidence interval for the population mean. (Round your answers to 2 decimal places.)
d. Develop the 99% confidence interval for the population mean. (Round your answers to 2 decimal places.)
e-1. Would it be reasonable to conclude that the population mean is 19 eggs?
Yes
No
e-2. What about 22 eggs?
Yes
No
5. As part of an annual review of its accounts, a discount brokerage selects a random sample of 28 customers. Their accounts are reviewed for total account valuation, which showed a mean of $42,900, with a sample standard deviation of $8,100. (Use t Distribution Table.) What is a 98% confidence interval for the mean account valuation of the population of customers? (Round your answers to the nearest dollar amount.)
6. You need to estimate the mean number of travel days per year for salespeople. The mean of a small pilot study was 150 days, with a standard deviation of 36 days. If you must estimate the population mean within 7 days, how many salespeople should you sample? Use the 90% confidence level. (Use z Distribution Table.) (Round your answer to the next whole number.)
7. The estimate of the population proportion should be within plus or minus 0.06, with a 95% level of confidence. The best estimate of the population proportion is 0.19. How large a sample is required? (Use z Distribution Table.) (Round up your answer to the next whole number.)
8. In a poll to estimate presidential popularity, each person in a random sample of 1,350 voters was asked to agree with one of the following statements:
The president is doing a good job.
The president is doing a poor job.
I have no opinion.
A total of 650 respondents selected the first statement, indicating they thought the president was doing a good job.
a. Construct a 98% confidence interval for the proportion of respondents who feel the president is doing a good job. (Round your answers to 3 decimal places.)
b. Based on your interval in part (a), is it reasonable to conclude that a majority of the population believes the president is doing a good job? Yes or No
9. Suppose the U.S. president wants to estimate the proportion of the population that supports his current policy toward revisions in the health care system. The president wants the estimate to be within 0.03 of the true proportion. Assume a 98% level of confidence. The president’s political advisors found a similar survey from two years ago that reported that 63% of people supported health care revisions. (Use z Distribution Table.)
a. How large of a sample is required? (Round up your answer to the next whole number.)
b. How large of a sample would be necessary if no estimate were available for the proportion supporting current policy? (Round up your answer to the next whole number.)
10. The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 500 viewers. After viewing the shows, 200 indicated they would watch the new show and suggested it replace the crime investigation show.
- Estimate the value of the population proportion.(Round your answers to 3 decimal places.)
- Develop a 99% confidence interval for the population proportion. (Use z Distribution Table.)(Round your answers to 3 decimal places.)
11. HighTech, Inc. randomly tests its employees about company policies. Last year in the 560 random tests conducted, 26 employees failed the test.
- Develop a 98% confidence interval for the proportion of applicants that fail the test.(Round your answers to 3 decimal places.)
- Would it be reasonable to conclude that 7% of the employees cannot pass the company policy test? Yes or No
12. Pharmaceutical companies promote their prescription drugs using television advertising. In a survey of 70 randomly sampled television viewers, 7 indicated that they asked their physician about using a prescription drug they saw advertised on TV.
- Develop a 90% confidence interval for the proportion of viewers who discussed a drug seen on TV with their physician.(Round your answers to 3 decimal places.)
- Is it reasonable to conclude that 20% of the viewers discuss an advertised drug with their physician?