Question

In: Math

Playbill magazine reported that the mean annual household income of its readers is $120,255. (Playbill, January...

Playbill magazine reported that the mean annual household income of its readers is $120,255. (Playbill, January 2006). Assume this estimate of the mean annual household income is based on a sample of 80 households, and based on past studies, the population standard deviation is known to be σ = $33,225.

a. Develop a 90% confidence interval estimate of the population mean.

b. Develop a 95% confidence interval estimate of the population mean.

c. Develop a 99% confidence interval estimate of the population mean.

d. Discuss what happens to the width of the confidence interval as the confidence level is increase. Does this result seem reasonable? Explain.

Solutions

Expert Solution

a)

90% confidence interval for is

- Z/2 * / sqrt(n) < < + Z/2 * / sqrt(n)

120255 - 1.645 * 33225 / sqrt(80) < < 120255 + 1.645 * 33225 / sqrt(80)

119643 < < 126366

b)

95% confidence interval for is

- Z/2 * / sqrt(n) < < + Z/2 * / sqrt(n)

120255 - 1.96 * 33225 / sqrt(80) < < 120255 + 1.96 * 33225 / sqrt(80)

112974 < < 1127536

c)

99% confidence interval for is

- Z/2 * / sqrt(n) < < + Z/2 * / sqrt(n)

120255 - 2.576 * 33225 / sqrt(80) < < 120255 + 2.576 * 33225 / sqrt(80)

110686 < < 129824

d)

When confidence level increases, the width of confidence interval increase.

milcah answered 11 months ago
Next > < Previous

Related Solutions

A magazine reported the mean annual household income of its readers to be $150,000 with a...
A magazine reported the mean annual household income of its readers to be $150,000 with a standard deviation of $30,000. A recent sample of 80 households from among those subscribing to this magazine found a mean of $139,155. What is the upper bound of a 95% confidence interval for the mean income (correct to no decimal places)?
Playbill magazine reported that the mean annual household income of its readers is $120,255. (Playbill, January...
Playbill magazine reported that the mean annual household income of its readers is $120,255. (Playbill, January 2006). Assume this estimate of the mean annual household income is based on a sample of 80 households, and based on past studies, the population standard deviation is known to be σ = $33,225. a. Develop a 90% confidence interval estimate of the population mean. b. Develop a 95% confidence interval estimate of the population mean. c. Develop a 99% confidence interval estimate of...
Farmer's Corporation made a report that the mean annual household income of its readers is $119,155...
Farmer's Corporation made a report that the mean annual household income of its readers is $119,155 (Thebill, March 2017). Assume this estimate of the mean annual household income is based on a sample of 80 households, and, based on past studies the population standard deviation is known to be σ = $30,000.00. Developed a 90% confidence interval estimate of the population mean Developed a 95% confidence interval estimate of the population mean. Developed a 99% confidence interval estimate of the...
Household Income in Maryland: According to Money magazine, Maryland had the highest median annual household income...
Household Income in Maryland: According to Money magazine, Maryland had the highest median annual household income of an state in 2018 at $75,847 (Time.com website). Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and a standard deviation of $33,800. a. What is the probability that a household in Maryland has an annual income of $100,000 or more? b. What is the probability that a household in Maryland has an annual income of...
According to Money magazine, Maryland had the highest median annual household income of any state in...
According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847.† Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800. (a) What is the probability that a household in Maryland has an annual income of $90,000 or more? (Round your answer to four decimal places.) (b) What is the probability that a household in Maryland has an annual income of...
4) A magazine reported the results of a survey in which readers were asked to send...
4) A magazine reported the results of a survey in which readers were asked to send their responses to several questions regarding good eating. DataSet for question 4,5,6 is the reported results to the question, How often do you eat chocolate? Based on the data answer the following questions. a) Were the responses to this survey obtained using voluntary sampling technique? Explain b) What type of bias may be present in the response? c) is 13% a reasonable estimate of...
According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847.
You may need to use the appropriate appendix table to answer this question. According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847. Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800. (a) What is the probability that a household in Maryland has an annual income of $90,000 or more? (Round your answer to four decimal places.) (b) What...
A travel magazine conducts an annual survey where readers rate their favorite cruise ship. Ships are...
A travel magazine conducts an annual survey where readers rate their favorite cruise ship. Ships are rated on a 10 point scale, with higher values indicating better service. A sample of 55 ships that carry fewer than 500 passengers resulted in a average rating of 6.36 with standard deviation 0.63. A sample of 25 ships that carry more than 500 passengers resulted in an average rating of 6.12 with standard deviation 0.78. Give a 95% confidence interval of the difference...
The Bureau of Economic Analysisin the U.S. Department of Commerce reported that the mean annual income...
The Bureau of Economic Analysisin the U.S. Department of Commerce reported that the mean annual income for a resident of North Carolina is $18,688 (USA Today, August 24, 1995). A researcher for the state of South Carolina wants to see if the mean annual income for a resident of South Carolina is different. A sample of 400 residents of South Carolina shows a sample mean annual income of $16,860 and the population standard deviation is assumed to known, =$14,624. Use...
The consumer food database contains five variables: Annual Food Spending per Household, Annual Household Income, Non-Mortgage...
The consumer food database contains five variables: Annual Food Spending per Household, Annual Household Income, Non-Mortgage Household Debt, Geographic Region of the U.S. of the Household, and Household Location. There are 200 entries for each variable in this database representing 200 different households from various regions and locations in the United States. Annual Food Spending per Household, Annual Household Income, and Non-Mortgage Household Debt are all given in dollars. The variable Region tells in which one of four regions the...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT