1- For a population data set, standard deviation=12.6. How large a sample should be selected so that the margin of error of estimate for 97% a confidence interval for =2.5 is ?

2- For a population data set,=13.0. How large a sample should be selected so that the margin of error of estimate for a95% confidence interval for is3.20?

3- A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of114

homeowners selected from this area showed that they pay an average of$1570

per month for their mortgages. The population standard deviation of such mortgages is$210

a.Find a97% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area. Round your answers to two decimal places.

b.Suppose the confidence interval obtained in partais too wide. Select all of the ways the width of this interval can be reduced.

Lowering the confidence level

Increasing the sample size

Increasing the confidence level

Lowering the sample size

4- A company that produces detergents wants to estimate the mean amount of detergent in64-ounce jugs at a99% confidence level. The company knows that the standard deviation of the amounts of detergent in all such jugs is0.23 ounce. How large a sample should the company take so that the estimate is within0.05 ounce of the population mean? Round your answer up to the nearest whole number.

5- a. Find the value oft for thet distribution with a sample size of16 and area in the left tail equal to0.10. Round your answer to 3 decimal places.

b. Find the value oft for thet distribution with a sample size of28 and area in the right tail equal to0.025. Round your answer to 3 decimal places.

6- A sample of18 observations taken from a normally distributed population produced the following data:

28.1, 27.5, 25.1, 25.3, 31.3, 23.1, 26.3, 24.2, 28.2, 37.2, 23.6, 28.7, 27.8, 25.1, 27.5, 25.1, 22.7, 22.8

Round your answers to three decimal places.

a.What is the point estimate of?

b.Make a98% confidence interval for.

c.What is the margin of error of estimate for in partb?

7- A random sample of20acres gave a mean yield of wheat equal to42.1 bushels per acre with a standard deviation of3 bushels. Assuming that the yield of wheat per acre is normally distributed, construct a90% confidence interval for the population mean. Round your answers to two decimal places.

8-A company randomly selected nine office employees and secretly monitored their computers for one month. The times (in hours) spent by these employees using their computers for non-job-related activities (playing games, personal communications, etc.) during this month are given below.

7, 13, 9, 8, 11, 4, 14, 1, 6

Assuming that such times for all employees are normally distributed, make a95% confidence interval for the corresponding population mean for all employees of this company. Round your answers to two decimal places.

9-A businesswoman is considering whether to open a coffee shop in a local shopping center. Before making this decision, she wants to know how much money people spend per week at coffee shops in that area. She took a random sample of26 customers from the area who visit coffee shops and asked them to record the amount of money (in dollars) they would spend during the next week at coffee shops. At the end of the week, she obtained the following data (in dollars) from these26 customers:

16.94, 38.73, 15.25, 14.37, 5.05, 63.67, 10.31, 13.16, 32.23, 36.13, 16.21, 65.92, 10.26, 37.01, 3.25, 6.97, 34.60, 6.34, 36.44, 27.63, 38.59, 13.31, 9.69, 9.42, 1.31, 5.20

Assume that the distribution of weekly expenditures at coffee shops by all customers who visit coffee shops in this area is approximately normal.

Round your answers to cents.

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

b.Make a90% confidence interval for the average amount of money spent per week at coffee shops by all customers who visit coffee shops in this area.

10- Check if the sample size is large enough to use the normal distribution to make a confidence interval forp

for the following case. n=55 andp^=0.08

11- A consumer agency wants to estimate the proportion of all drivers who wear seat belts while driving. What is the most conservative estimate of the sample size that would limit the margin of error to within0.28 of the population proportion for a99% confidence interval? Round your answer up to the nearest whole number.

12- A sample of1100 observations taken from a population produced a sample proportion of0.33. Make a90% confidence interval forp. Round your answers to three decimal places. The true population proportion for this population is0.34. Does the confidence interval constructed cover this population proportion?

The confidence interval:

covers or does not cover the true population proportion.

13- A sample selected from a population gave a sample proportion equal to0.66. Round your answers to three decimal places.

a.Make a97%confidence interval forp assumingn=100.

b.Construct a97% confidence interval forp assumingn=550.

c.Make a97% confidence interval forp assumingn=1275.

d.Does the width of the confidence intervals constructed in partsathroughcdecrease as the sample size increases?

14- According to a Pew Research Center nationwide telephone survey of adults conducted March 15 to April 24, 2011,69% of college graduates said that their college education gave them maturity (Time, May 30, 2011). Suppose that this survey includedn=1365 college graduates.

a.What is the point estimate of the corresponding population proportion?

b.Construct a90% confidence interval for the proportion of all college graduates who will say that their college education gave them maturity. What is the margin of error for this estimate? Round your answers to three decimal places.

15- It is said that happy and healthy workers are efficient and productive. A company that manufactures exercising machines wanted to know the percentage of large companies that provide on-site health club facilities. A sample of240 such companies showed that97 of them provide such facilities on site. Construct a90% confidence interval for the percentage of all such companies that provide such facilities on site. What is the margin of error for this estimate? Round your answers to one decimal place.