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Exam 8: Interval Estimation

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Question 1

Multiple Choice

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Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, she has garnered 51% support. Construct a 95% confidence interval on the population proportion for the support of candidate A in the following election.

A) [0.4534, 0.5666]
B) [0.4625, 0.5575]
C) [0.5084, 0.5116]
D) [0.5086, 0.5114]

E) A) and D)
F) None of the above

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Question 2

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A sample of 2,007 American adults was asked how they viewed China, with 17% of respondents calling the country "unfriendly" and 6% of respondents indicating the country was "an enemy." Construct a 99% confidence interval of the proportion of American adults who viewed China as "an enemy."

A) [0.0463, 0.0737]
B) [0.0476, 0.0724]
C) [0.0512, 0.0688]
D) [0.0597, 0.0603]

E) All of the above
F) B) and D)

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Question 3

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The confidence coefficient is equal to ________.

A confidence interval provides a value that, with a certain measure of confidence, is the population parameter of interest.

The Retail Advertising and Marketing Association would like to estimate the average amount of money that a person spends for Mother's Day with 99% confidence interval and a margin of error within plus or minus $6. Assuming the standard deviation for spending on Mother's Day is $36, the required sample size is ________.

A Monster.com pool of 3,057 individuals asked: "What's the longest vacation you plan to take this summer?" The following relative frequency distribution summarizes the results. The 99% confidence interval for the proportion of people who plan a one-week or two-week vacation this summer is ________.

Pure-bred dogs competing in shows must often meet specific height criteria to be within the breed standard. A new breed of dog, the pug-cock-a-poo, has been approved by a kennel club. To establish the breed standard, the organization of breeders has taken the height from a sample of 25 pug-cock-a-poos and found the sample mean to equal 14 inches. The variance of this sample is 2.25. A) Construct a 90% confidence interval for the population mean height of the pug-cock-a-poos. B) What assumption is necessary for constructing the aforementioned interval?

Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, 98 supported candidate B and 58 supported candidate C. Construct a 99% confidence interval on the population proportion for the support of candidate A in the following election.

What is the most typical form of a calculated confidence interval?

A sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year. Construct a 98% confidence interval of the proportion of American households who expect to buy a new car next year.

For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known?

Bobby does not want to be late to work again. He drives to work every morning from Oakland to San Francisco and crossing the Bay Bridge seems to take forever. He times himself crossing the bridge for seven consecutive mornings, with the resulting times of 22.34, 27.54, 15.26, 13.56, 18.57, 21.22, and 19.08 minutes. Construct a 99% confidence interval from those times.

Find the minimum sample size when we want to construct a 90% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a preselected poll of 100 residents, 22 supported her. The desired margin of error is 0.08.

The t_df distribution is similar to the z distribution because ________.

At an academically challenging high school, the average GPA of a high school senior is known to be normally distributed with a variance of 0.25. A sample of 20 seniors is taken and their average GPA is found to be 2.71. Develop a 90% confidence interval for the population mean GPA.

Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s) : 549,449,705,529,639,609. Find a 95% confidence interval for the mean sale price in San Luis Obispo County.

A sample of holiday shoppers is taken randomly from a local mall. Forty-nine shoppers were selected and asked what their average spending on gifts would be during the entire holiday season. The point estimate of the population mean was calculated as $550 and the sample standard deviation was calculated as $92. A) Construct a 95% confidence interval of the population mean spending. B) Explain how the central limit theorem is used in constructing this interval.

The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S. economy in many ways, but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure, and lenders became more wary of filing faulty documentation. Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed, transferring the property) has been 230 days, 420 days, 340 days, 367 days, 295 days, 314 days, 385 days, and 311 days. Assume the duration is normally distributed. Construct a 99% confidence interval for the mean duration of the foreclosure process in Boston.

Newscasters wish to predict the outcome of the next presidential election with 95% confidence and a margin of error equal to 0.08. Find the appropriate sample size to accomplish this goal.

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is D = 1.25? The standard deviation in a preselected sample is 8.5.