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

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

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

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

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

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

milcah answered 5 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...

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 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...

What is the predicted annual credit card charge for a three-person household with an annual income...

What is the predicted annual credit card charge for a three-person household with an annual income of $40,000 (show your work) - Income ($1000s) Household Size Amount Charged ($) 54 3 4,016 30 2 3,159 32 4 5,100 50 5 4,742 31 2 1,864 55 2 4,070 37 1 2,731 40 2 3,348 66 4 4,764 51 3 4,110 25 3 4,208 48 4 4,219 27 1 2,477 33 2 2,514 65 3 4,214 63 4 4,965 42 6 4,412...

Assume that Thailand's government reports its population mean disposable household income is $900 per month, with...

Assume that Thailand's government reports its population mean disposable household income is $900 per month, with a standard deviation of $100. Indonesia's population mean is $1,000, with a standard deviation of $300. a. Which country has more variation in income? Explain using popular phrases, such as “gap between rich and poor.” b. Each country defines the poverty level to be $750. If you assume that income has a normal distribution, find the probability that a household’s income is below the...

Subjects