stats

copy_of_assignment_9.xlsx

8.1 #1

8.1 #1
A simple random sample of 40 items resulted in a sample mean of 25.
The population standard deviation is Ç =5.
a) What is the standard error of the mean,				?
b) At the 95% confidenc level, what is the margin of error?

8.1 #2

A simple random sample of 60 items resulted in a sample mean of 80.

The population standard deviation is Ç =15.

a) Compute the 95% confidence interval for the population mean.

b) Assume the sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean.

c) What is the effect of a larger sample size on the interval estimate?

8.1 #3

A survey of 35 restaurants in the Fast Food/Pizza group showed a sample mean customer satisfaction index of 71.

Past data indicate that the population standard deviation of the index has been relatively stable with Ç = 5.

a) At 99% confidence, what is the margin of error?

b) Construct the 99% confidence interval.

8.2 #4

Find the t value(s) for each of the following cases.

a) Upper tail area of 0.025 with 12 degrees of freedom.

b) Lower tail area of 0.05 with 50 degrees of freedom.

c) Upper tail area of 0.01 with 30 degrees of freedom.

d) Where 90% of the area falls between these two t values with 25 degrees of freedom.

8.2 #5

A simple random sample with n = 54 provided a sample mean of 22.5 and a sample standard deviation of 4.4.

a) Develop a 90% confidence interval for the population mean.

b) Develop a 99% confidence interval for the population mean.

c) What happens the to width of the confidence interval as the confidence level is increased?

8.2 #6

The mean number of hours of flying time for pilots at Continental Airlines is 49 hours per month.

Assume this mean was based on actual flying times for a sample of 100 Continental pilots and

that the sample standard deviation was 8.5 hours.

a) At 95% confidence, what is the margin of error?

b) Construct the 99% confidence interval?

8.3 #7

How large a sample should be selected to provide a 95% confidence interval with a margin of error of 10?

Assume that the population standard deviation is 40.

8.3 #8

The average cost of a gallon of unleaded gasoline is $2.41. Assume the standard deviation is $.15 and suppose we

wish to report at the 95% confidence level.

What minimum sample size is needed if:

a) The desired margin of error is $0.07

b) The desired margin of error is $.02

c) What happens to the sample size as the margin of error is decreased?

8.4 #9

A simple random sample of 800 elements generates a sample proportion of

a) Provide a 90% confidence interval for the population proportion.

b) Provide a 95% confidence interval for the population proportion.

8.4 #10

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.3

for the estimation of a population proportion?

a) Assume that past data are not available for developing a planning value for p*.

b) Assume that past data available reveals p* = 0.85.

8.5 #11

8.4 #11

A surprising number of motor vehicles are not covered by insurance. Sample results showed that 46 of 200

vehicles were not covered by insurance.

a) What is the point estimate of the proportion of vehicles not covered by insurance?

b) Develop a 95% confidence interval for the population proportion.