# Statistics: Problems

1. For a t distribution with 16 degrees of freedom, find the area, or probability, in each region.

a. To the right of 2.120. (Use 3 decimals.) __________

b. To the left of 1.337. (Use 2 decimals.) __________

c. To the left of -1.746. (Use 2 decimals.) __________

d. To the right of 2.583. (Use 2 decimals.) __________

e. Between -2.120 and 2.120. (Use 2 decimals.) __________

f. Between -1.746 and 1.746. (Use 2 decimals.) __________

2. The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5.

a. What is the point estimate of the population mean? __________

b. What is the point estimate of the population standard deviation (to 2 decimals)? __________

c. With 95% confidence, what is the margin of error for the estimation of the population mean (to 1 decimal)? __________

d. What is the 95% confidence interval for the population mean (to 1 decimal)?

( __________ , __________ )

3. Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2. Provide 90% and 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel.

90% Confidence, to 2 decimals:

( __________ , __________ )

95% Confidence, to 2 decimals:

( __________ , __________ )

4. The average cost per night of a hotel room in New York City is $273 (SmartMoney, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard deviation is $65.

a. With 95% confidence, what is the margin of error (to 2 decimals)?

_________________

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

( _________________ , _________________ )

c. Two years ago the average cost of a hotel room in New York City was $229. Discuss the change in cost over the two-year period.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

_________________

5. How large a sample should be selected to provide a 95% confidence interval with a margin of error of 10 (to the nearest whole number)? Assume that the population standard deviation is 40.

__________

6. Use 6.84 days as a planning value for the population standard deviation.

a. Assuming 95% confidence, what sample size would be required to obtain a margin of error of 1.5 days (to the nearest whole number)? __________

b. Assuming 90% confidence, what sample size would be required to obtain a margin of error of 2 days (to the nearest whole number)? __________

7. Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation (to the nearest whole number)?

__________

How large a sample should be taken if the desired margin of error is as shown below (to the nearest whole number)?

a. $500? __________

b. $200? __________

c. $100? __________

d. Would you recommend trying to obtain the $100 margin of error?

_________________

8. The travel-to-work time for residents of the 15 largest cities in the United States is reported in the 2003 Information Please Almanac. Suppose that a preliminary simple random sample of residents of San Francisco is used to develop a planning value of 6.45 minutes for the population standard deviation.

If we want to estimate the population mean travel-to-work time for San Francisco residents with a margin of error of 2 minutes, what sample size should be used? Assume 95% confidence.

__________

If we want to estimate the population mean travel-to-work time for San Francisco residents with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.

__________

#### Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Statistics and provides students with a clear perspective of the underlying concepts.