Question

In: Statistics and Probability

You are given the sample mean and the population standard deviation. Use this information to construct...

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals. A random sample of 45 home theater systems has a mean price of ​$120.00. Assume the population standard deviation is ​$17.50.

Solutions

Expert Solution

Solution:

The 90% and 95% confidence intervals for the population mean by using excel are given as below:

90% Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

17.5

Sample Mean

120

Sample Size

45

Confidence Level

90%

Intermediate Calculations

Standard Error of the Mean

2.6087

Z Value

-1.6449

Interval Half Width

4.2910

Confidence Interval

Interval Lower Limit

115.71

Interval Upper Limit

124.29

95% Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

17.5

Sample Mean

120

Sample Size

45

Confidence Level

95%

Intermediate Calculations

Standard Error of the Mean

2.6087

Z Value

-1.9600

Interval Half Width

5.1130

Confidence Interval

Interval Lower Limit

114.89

Interval Upper Limit

125.11

From above two observations, it is observed as we increase the confidence level, the margin of error increase, and therefore width of the confidence interval increases.


Related Solutions

You are given the sample mean and the population standard deviation. Use this information to construct...
You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of 35 business​ days, the mean closing price of a certain stock was ​$109.47. Assume the population standard deviation is ​$10.14. please answer both questions, thank you
You are given the sample mean and the population standard deviation. Use this information to construct...
You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of 32 business​ days, the mean closing price of a certain stock was ​$111.22. Assume the population standard deviation is ​$10.51. The​ 90% confidence interval is ​( nothing​, nothing​). ​(Round to two decimal places as​ needed.) The​ 95% confidence...
You are given the sample mean and the population standard deviation. Use this information to construct...
You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Which interval is​ wider? If​ convenient, use technology to construct the confidence intervals. A random sample of 49 gas grills has a mean price of $631.60. Assume the population standard deviation is $55.70.
You are given the sample mean and the population standard deviation. Use this information to construct...
You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Which interval is​ wider? If​ convenient, use technology to construct the confidence intervals. A random sample of 3232 gas grills has a mean price of ​$642.50642.50. Assume the population standard deviation is ​$59.1059.10. the 90% confidence interval is?? the 95% confidence interval is?? which interval is wider?
You are given the sample mean and the population standard deviation. Use this information to construct...
You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals. A random sample of 55 home theater systems has a mean price of ​$136.00. Assume the population standard deviation is ​$18.60. a) The​ 90% confidence interval is ​____ b) The​ 95% confidence interval is...
You are given the sample mean of the population standard deviation use the information to construct...
You are given the sample mean of the population standard deviation use the information to construct a 90% and a 95% confidence interval for the population mean interpret the results and compare the widths Of the confidence intervals. from random sample of 42 business days The meme closing price of a certain stock was $122.81. assume the population standard deviation is $10.64 The 90% confidence interval is____? as well for 95%
You are given the sample mean and the population standard deviation. Use this information to construct...
You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of 37 business​ days, the mean closing price of a certain stock was ​$118.77. Assume the population standard deviation is ​$11.26. The​ 90% confidence interval is
You are given the sample mean and the population standard deviation. Use this information to construct...
You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Which interval is​ wider? If​ convenient, use technology to construct the confidence intervals. A random sample of 43 gas grills has a mean price of ​$626.90. Assume the population standard deviation is ​$56.60. The​ 90% confidence interval is ​. ​(Round to one decimal place as​ needed.) The​ 95% confidence interval is ​. ​(Round to...
You are given the sample mean and the population standard deviation. Use this information to construct...
You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals. A random sample of 6060 home theater systems has a mean price of ​$135.00135.00. Assume the population standard deviation is ​$15.8015.80. Construct a​ 90% confidence interval for the population mean. The​ 90% confidence interval...
You are given the sample mean and the population standard deviation. Use this information to construct...
You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. A random sample of 35 home theater systems has a mean price of ​$125.00.  Assume the population standard deviation is ​$19.60
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT