## Introductory Statistics

Statistics

## Quiz 8 :

Estimation of the Mean and Proportion

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Q25 Q25 Q25

A random sample of 23 tourists who visited Hawaii this summer spent an average of $1,456.0 on this trip with a standard deviation of $263.00.Assuming that the money spent by all tourists who visit Hawaii has an approximate normal distribution,the 95% confidence interval for the average amount of money spent by all tourists who visit Hawaii,rounded to two decimal places,is:

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Q26 Q26 Q26

A random sample of 12 life insurance policy holders showed that the mean value of their life insurance policies is $210,000 with a standard deviation of $44,600.Assuming that the values of life insurance policies for all such policy holders are approximately normally distributed,the 99% confidence interval for the mean value of all life insurance policies,rounded to two decimal places,is:

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Q27 Q27 Q27

A random sample of 8 houses selected from a city showed that the mean size of these houses is 1,881.0 square feet with a standard deviation of 328.00 square feet.Assuming that the sizes of all houses in this city have an approximate normal distribution,the 90% confidence interval for the mean size of all houses in this city,rounded to two decimal places,is:

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Q32 Q32 Q32

A random sample of 983 families selected from a large city showed that 17.5% of them make $100,000 or more per year.Based on this sample,the 99% confidence interval for the proportion of all families living in this city who make $100,000 or more per year,rounded to four decimal places,is:

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Q34 Q34 Q34

A researcher wants to make a 99% confidence interval for a population mean.She wants the margin of error to be within 4.6 of the population mean.The population standard deviation is 18.22.The sample size that will yield a margin of error within 4.6 of the population mean is:

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Q35 Q35 Q35

A researcher wants to make a 95% confidence interval for a population mean.She wants the margin of error to be within 1.9 of the population mean.The population standard deviation is 11.07.The sample size that will yield a margin of error within 1.9 of the population mean is:

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Q36 Q36 Q36

A researcher wants to estimate the mean age of all Business Week readers at a 99% confidence level.She wants the margin of error to be within 3.1 years of the population mean.The standard deviation of ages of all Business Week readers is 10.04 years.The sample size that will yield a margin of error within 3.1 of the population mean is:

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Q37 Q37 Q37

A company wants to estimate the mean net weight of all 32-ounce packages of its Yummy Taste cookies at a 95% confidence level.The margin of error is to be within 0.025 ounces of the population mean.The population standard deviation is 0.096 ounces.The sample size that will yield a margin of error within 0.025 ounces of the population mean is:

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Q40 Q40 Q40

A company wants to estimate,at a 95% confidence level,the proportion of all families who own its product.A preliminary sample showed that 30.0% of the families in this sample own this company's product.The sample size that would limit the margin of error to be within 0.045 of the population proportion is:

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Q43 Q43 Q43

The Labor Bureau wants to estimate,at a 90% confidence level,the proportion of all households that receive welfare.A preliminary sample showed that 18.5% of households in this sample receive welfare.The sample size that would limit the margin of error to be within 0.036 of the population proportion is:

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Q45 Q45 Q45

You are estimating the mean waiting time in line at a particular fast-food restaurant.You ask 30 customers,at varying times of the day,how long they waited in line before placing their order.You then take the average of these values and use this average to estimate the mean waiting time for all customers.The average of the 30 values is an example of a(n):

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Q46 Q46 Q46

A scientist is estimating the mean lifetime of a newly-discovered insect.From a sample of 88 insects,she finds a sample mean of 49.2 days.Suppose that the population standard deviation of all lifetimes is 2.500 days.What are the boundaries for a 90% confidence interval for the mean lifetime of the insect,rounded to two decimal places?

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Q47 Q47 Q47

The Eks Survey Company employs 2000 people to conduct telephone surveys.Because many people don't like to answer such surveys,many "hang-ups" (whereby the person hangs up without completing the survey)occur.The owner of Eks wants to determine the mean number of "hang-ups" per employee on a particular day,using 95% confidence.He samples 50 employees,and finds that the mean number of "hang-ups" on that day was 41.0.Suppose that the standard deviation of the number of "hang-ups" for all employees is 21.8 What is the value of the margin of error? (round to four decimal places)

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Q51 Q51 Q51

Each employee of a large company is encouraged to contribute,through payroll deduction,to an international charity.Annual contributions per employee follow (approximately)a normal distribution.You take a random sample of 25 employees and find that the sample mean annual contribution per employee is $501 with a standard deviation of $17.00.What are the boundaries for a 99% confidence interval for the population mean,rounded to two decimal places?

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Q52 Q52 Q52

In a 1997 poll of 261 male,married,upper-level managers conducted by Joy Schneer and Frieda Reitman for Fortune magazine,31% of the men stated that their wives worked either full-time or part-time (Fortune,March 17,1997).What are the boundaries for a 99% confidence interval for p,the proportion of all male,married,upper-level managers whose wives work?

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Q53 Q53 Q53

An advisor to the mayor of a large city wants to estimate,within 2.450 minutes,the mean travel time to work for all employees who work within the city limits.He knows that the standard deviation of all travel times is 11.35 minutes.He also wants to achieve a 95% confidence interval.He will poll a random sample of city employees.How many employees should he poll?

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Q55 Q55 Q55

An employee of the College Board analyzed the mathematics section of the SAT for 97 students and finds = 30.2 and s = 13.0.She reports that a 97% confidence interval for the mean number of correct answers is (27.336,33.064).Does the interval (27.336,33.064)cover the true mean?
Which of the following alternatives is the best answer for the above question?
A)Yes,(27.336,33.064)covers the true mean.
B)No,(27.336,33.064)does not cover the true mean.
C)We will never know whether (27.336,33.064)covers the true mean.
D)The true mean will never be in (27.336,33.064).

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