## Statistics for Management

Statistics

## Quiz 10 :

Introduction to Estimation

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Q26 Q26 Q26

The librarian at the New York City Public Library has asked her assistant for an interval estimate of the mean number of books checked out each day.The assistant took a sample and found the mean to be 880 books.She provides the librarian with an interval estimate of between 790 and 970 books checked out per day.An efficient, unbiased point estimate of the number of books checked out each day at the New York City Public Library is:

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Multiple Choice

Q46 Q46 Q46

A random sample of 10 university students was surveyed to help estimate the average amount of time students spent per week on their computers.The student hours spent using a personal computer over a randomly selected week were 13, 14, 5, 6, 8, 10, 7, 12, 15, 3.
a.
Find an unbiased estimator of the average time per week for all university students.
b.
Find an unbiased estimator of the variance.
c.
Find a consistent estimator of the average time per week for all university students.

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Q88 Q88 Q88

It is desired to estimate the average total compensation of CEOs in the publishing industry.Data were randomly collected from 18 CEOs and 95% confidence interval was calculated to be ($2,190,000, $4,720,000).Based on the interval above, do you believe the actual average total compensation of CEOs in the publishing industry could be $3,000,000?

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Multiple Choice

Q101 Q101 Q101

A survey of 100 businesses revealed that the mean after-tax profit was $80,000.Assume the population standard deviation is $15,000:
a.
Determine the 95% confidence interval estimate of the mean after-tax profit for all businesses.
b.
Explain why you can use the confidence interval formula here, even though the population is not necessarily normal.

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Q103 Q103 Q103

A sample of 49 measurements of tensile strength for roof hangers are calculated to have a mean of 2.45 and a standard deviation of 0.25.(Units are Newton's per square meter.)
a.
Determine the 95% confidence interval for mean tensile strength for all hangers.
b.
Interpret this confidence interval.

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Q104 Q104 Q104

A random sample of 10 waiters in Weston, West Virginia, revealed the following hourly earnings, including tips: 19, 18, 15, 16, 18, 17, 16, 18, 20, and 14.(Units are dollars.)
a.
If the hourly earnings are normally distributed with a standard deviation of $4.50, estimate with 95% confidence the mean hourly earnings for all waitresses in Iowa City.
b.
Interpret your confidence interval.

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Q105 Q105 Q105

Time Spent Playing Computer Games
Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.
-{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean.

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Q106 Q106 Q106

Time Spent Playing Computer Games
Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.
-{Time Spent Playing Computer Games Narrative} Interpret the 95% confidence interval for this situation.

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Q107 Q107 Q107

Time Spent Playing Computer Games
Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.
-{Time Spent Playing Computer Games Narrative} Determine and interpret the 99% confidence interval estimate of the population mean.

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Q108 Q108 Q108

Time Spent Playing Computer Games
Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.
-{Time Spent Playing Computer Games Narrative} Determine and interpret the 90% confidence interval estimate of the population mean.

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Q109 Q109 Q109

Time Spent Playing Computer Games
Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.
-{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the sample size is changed to 300.

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Q110 Q110 Q110

Time Spent Playing Computer Games
Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.
-{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the sample size is changed to 36.

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Q111 Q111 Q111

Time Spent Playing Computer Games
Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.
-{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the population standard deviation is changed to 2.

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Q112 Q112 Q112

Time Spent Playing Computer Games
Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.
-{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the population standard deviation is changed to 1.2.

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Q113 Q113 Q113

Time Spent Playing Computer Games
Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.
-{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the sample mean is changed to 5.0 hours.

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Q114 Q114 Q114

Time Spent Playing Computer Games
Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.
-{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the sample mean is changed to 8.5 hours.

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Q115 Q115 Q115

A random sample of 10 university students was surveyed to determine the amount of time spent weekly at the library.The times are: 13, 14, 5, 6, 8, 10, 7, 12, 15, and 3.If the times are normally distributed with a standard deviation of 5.2 hours, estimate with 90% confidence the mean weekly time at the library by all university students.

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Q117 Q117 Q117

A market researcher is interested in studying the incomes of consumers in a particular region.The population standard deviation is known to be $1,000.A random sample of 50 individuals resulted in an average income of $15,000.What is the upper end point in a 99% confidence interval for the average income?

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Q118 Q118 Q118

An economist is interested in studying the spending habits of consumers in a particular region.The population standard deviation is known to be $1,000.A random sample of 50 individuals resulted in an average expense of $15,000.What is the width of the 99% confidence interval?

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Q119 Q119 Q119

A precision control engineer is interested in the mean length of tubing being cut automatically by machine.It is known that the standard deviation in the cutting length is 0.15 feet.A sample of 60 cut tubes yields a mean length of 12.15 feet.This sample will be used to obtain a 99% confidence interval for the mean length cut by machine.
a.
What is the z

_{}_{ / 2}value to use in obtaining the confidence interval? b. Develop the 99% confidence interval for .Free

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Q148 Q148 Q148

College Dean
A college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200.
-{College Dean Narrative} What sample size should be used if we wish to estimate the population mean to within 10 units?

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Q149 Q149 Q149

A research firm has been contracted to estimate the mean weekly family expenditure on clothes.He believes that the standard deviation of the weekly expenditure is $125.Determine with 99% confidence the number of families that must be sampled to estimate the mean weekly family expenditure on clothes to within $15.

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Q151 Q151 Q151

An electronics retailer is interested in studying the incomes of consumers in a particular area.The population standard deviation is known to be $1,000.What sample size would the researcher need to use for a 95% confidence interval if the difference between UCL and LCL should not be more than $100?

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Q152 Q152 Q152

An engineer for an electric fencing company is interested in the mean length of wires being cut automatically by machine.The desired length of the wires is 12 feet.It is known that the standard deviation in the cutting length is 0.15 feet.Suppose the engineer decided to estimate the mean length to within 0.025 with 99% confidence.What sample size would be needed?

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