Exam 8: Sampling Distributions and Estimation

Fulsome University has 16,059 students.In a sample of 200 students,12 were born outside the United States.Construct a 95 percent confidence interval for the true population proportion.How large a sample is needed to estimate the true proportion of Fulsome students who were born outside the United States with an error of ± 2.5 percent and 95 percent confidence? Show your work and explain fully.

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Question 1

Correct Answer:

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The 95 percent confidence interval is p ± z0.025[p(1 − p)/n]1/2 = 0.06 ± (1.960)[(0.06)(0.94)/200]1/2 or 0.06 ± 0.032914 or = 0.027 < π < 0.093.To reduce the error to 0.025,the required sample size is n = p(1 − p)so
n = (0.06)(0.94)= 346.7,or n = 347 (rounded up).
We have a sample value for p,so we do not need to assume that π = 0.50.If you did assume π = 0.50,you would get an unnecessarily large required sample since the preliminary sample indicates that π is not 0.50.The sample does not exceed 5 percent of the population size,so the finite population correction would make little difference.

To narrow the confidence interval for π,we can either increase n or decrease the level of confidence.

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Question 2

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True

The statistic p = x/n may be assumed normally distributed when np ≥ 10 and n(1 − p)≥ 10.

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Question 3

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True

For a given sample size,the higher the confidence level,the

(Multiple Choice)

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Question 4

To estimate a proportion with a 4 percent margin of error and a 95 percent confidence level,the required sample size is over 800.

(True/False)

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Question 5

For a sample of size 11,the critical values of chi-square for a 90 percent confidence interval for the population variance are

(Multiple Choice)

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Question 6

Which statement is incorrect? Explain.

(Multiple Choice)

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Question 7

To determine a 72 percent level of confidence for a proportion,the value of z is approximately

(Multiple Choice)

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Question 8

Professor York randomly surveyed 240 students at Oxnard University and found that 150 of the students surveyed watch more than 10 hours of television weekly.How many additional students would Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ± 3 percent with 99 percent confidence?

(Multiple Choice)

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Question 9

Ceteris paribus,the narrowest confidence interval for π is achieved when p = 0.50.

(True/False)

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Question 10

A random sample of 160 commercial customers of PayMor Lumber revealed that 32 had paid their accounts within a month of billing.The 95 percent confidence interval for the true proportion of customers who pay within a month would be

(Multiple Choice)

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Question 11

In constructing confidence intervals,it is conservative to use the z distribution when n ≥ 30.

(True/False)

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Question 12

A highway inspector needs an estimate of the mean weight of trucks crossing a bridge on the interstate highway system.She selects a random sample of 49 trucks and finds a mean of 15.8 tons with a sample standard deviation of 3.85 tons.The 90 percent confidence interval for the population mean is

(Multiple Choice)

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Question 13

The distribution of the sample proportion p = x/n is normal when n ≥ 30.

(True/False)

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Question 14

The finite population correction factor (FPCF)can be ignored if n = 7 and N = 700.

(True/False)

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Question 15

In which situation may the sample proportion safely be assumed to follow a normal distribution?

(Multiple Choice)

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Question 16

In a confidence interval,the finite population correction factor (FPCF)can be ignored when

(Multiple Choice)

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Question 17

A company wants to estimate the time its trucks take to drive from city A to city B.The standard deviation is known to be 12 minutes.What sample size is required so that the error does not exceed ±2 minutes,with 95 percent confidence?

(Multiple Choice)

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Question 18

If σ = 25,find the sample size to estimate the mean with an error of ± 3 and 90 percent confidence (rounded to the next higher integer).

(Multiple Choice)

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Question 19

When the sample standard deviation is used to construct a confidence interval for the mean,we would use the Student's t distribution instead of the normal distribution.

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Question 20

Showing 1 - 20 of 107

To narrow the confidence interval for π,we can either increase n or decrease the level of confidence.

The statistic p = x/n may be assumed normally distributed when np ≥ 10 and n(1 − p)≥ 10.

For a given sample size,the higher the confidence level,the

To estimate a proportion with a 4 percent margin of error and a 95 percent confidence level,the required sample size is over 800.

For a sample of size 11,the critical values of chi-square for a 90 percent confidence interval for the population variance are

Which statement is incorrect? Explain.

To determine a 72 percent level of confidence for a proportion,the value of z is approximately

Ceteris paribus,the narrowest confidence interval for π is achieved when p = 0.50.

A random sample of 160 commercial customers of PayMor Lumber revealed that 32 had paid their accounts within a month of billing.The 95 percent confidence interval for the true proportion of customers who pay within a month would be

In constructing confidence intervals,it is conservative to use the z distribution when n ≥ 30.

A highway inspector needs an estimate of the mean weight of trucks crossing a bridge on the interstate highway system.She selects a random sample of 49 trucks and finds a mean of 15.8 tons with a sample standard deviation of 3.85 tons.The 90 percent confidence interval for the population mean is

The distribution of the sample proportion p = x/n is normal when n ≥ 30.

The finite population correction factor (FPCF)can be ignored if n = 7 and N = 700.

In which situation may the sample proportion safely be assumed to follow a normal distribution?

In a confidence interval,the finite population correction factor (FPCF)can be ignored when

A company wants to estimate the time its trucks take to drive from city A to city B.The standard deviation is known to be 12 minutes.What sample size is required so that the error does not exceed ±2 minutes,with 95 percent confidence?

If σ = 25,find the sample size to estimate the mean with an error of ± 3 and 90 percent confidence (rounded to the next higher integer).

When the sample standard deviation is used to construct a confidence interval for the mean,we would use the Student's t distribution instead of the normal distribution.

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