Question 1

A sample of size 5 shows a mean of 45.2 and a sample standard deviation of 6.4.The standard error of the sample mean is approximately 2.86.

Accepted Answer

A) True 
 B)False

Question 2

A 95 percent confidence interval constructed around p will be wider than a 90 percent confidence interval.

Accepted Answer

A) True 
 B)False

Question 3

Sampling variation is not controllable by the statistician.

Accepted Answer

A) True 
 B)False

Question 4

In constructing a 95 percent confidence interval,if you increase n to 4n,the width of your confidence interval will (assuming other things remain the same)be:

Accepted Answer

A)  about 25 percent of its former width. 
B)  about two times wider. 
C)  about 50 percent of its former width. 
D)  about four times wider. 
A)  about 25 percent of its former width. 
B)  about two times wider. 
C)  about 50 percent of its former width. 
D)  about four times wider.

Question 5

To estimate the average annual expenses of students on books and class materials a sample of size 36 is taken.The sample mean is $850 and the sample standard deviation is $54.A 99 percent confidence interval for the population mean is:

Accepted Answer

A)  $823.72 to $876.28 
B)  $832.36 to $867.64 
C)  $826.82 to $873.18 
D)  $825.48 to $874.52 
A)  $823.72 to $876.28 
B)  $832.36 to $867.64 
C)  $826.82 to $873.18 
D)  $825.48 to $874.52

Question 6

The confidence interval half-width when π = .50 is called the margin of error.

Accepted Answer

A) True 
 B)False

Question 7

The Central Limit Theorem (CLT):

Accepted Answer

A)  applies only to samples from normal populations. 
B)  applies to any population. 
C)  applies best to populations that are skewed. 
D)  applies only when μ and σ are known. 
A)  applies only to samples from normal populations. 
B)  applies to any population. 
C)  applies best to populations that are skewed. 
D)  applies only when μ and σ are known.

Question 8

To estimate π,you typically need a sample size equal to at least 5 percent of your population.

Accepted Answer

A) True 
 B)False

Question 9

The Central Limit Theorem guarantees an approximately normal sampling distribution when n is sufficiently large.

Accepted Answer

A) True 
 B)False

Question 10

The width of a confidence interval for μ is not affected by:

Accepted Answer

A)  the sample size. 
B)  the confidence level. 
C)  the standard deviation. 
D)  the sample mean. 
A)  the sample size. 
B)  the confidence level. 
C)  the standard deviation. 
D)  the sample mean.

Question 11

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

Accepted Answer

A)  more accurate the point estimate. 
B)  smaller the standard error. 
C)  smaller the interval width. 
D)  greater the interval width. 
A)  more accurate the point estimate. 
B)  smaller the standard error. 
C)  smaller the interval width. 
D)  greater the interval width.

Question 12

A random sample of 16 ATM transactions at the Last National Bank of Flat Rock revealed a mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes.The width (in minutes)of the 95 percent confidence interval for the true mean transaction time is:

Accepted Answer

A)  ± 0.639 
B)  ± 0.588 
C)  ± 0.300 
D)  ± 2.131 
A)  ± 0.639 
B)  ± 0.588 
C)  ± 0.300 
D)  ± 2.131

Question 13

Read the news story below.Using the 95 percent confidence level,what sample size would be needed to estimate the true proportion of stores selling cigarettes to minors with an error of ± 3 percent? Explain carefully,showing all steps in your reasoning.

Accepted Answer

@#IMG-DLM& = @#IMG-DLM& = 813.5,or 814 (rounded up

Question 14

The efficiency of an estimator depends on the variance of the estimator's sampling distribution.

Accepted Answer

A) True 
 B)False

Question 15

A higher confidence level leads to a narrower confidence interval,ceteris paribus.

Accepted Answer

A) True 
 B)False

Question 16

A university wants to estimate the average distance that commuter students travel to get to class with an error of ± 3 miles and 90 percent confidence.What sample size would be needed,assuming that travel distances are normally distributed with a range of X = 0 to X = 50 miles,using the Empirical Rule μ ± 3σ to estimate σ.

Accepted Answer

A)  About 28 students 
B)  About 47 students 
C)  About 30 students 
D)  About 21 students 
A)  About 28 students 
B)  About 47 students 
C)  About 30 students 
D)  About 21 students

Question 17

The Central Limit Theorem says that a histogram of the sample means will have a bell shape,even if the population is skewed and the sample is small.

Accepted Answer

A) True 
 B)False

Question 18

In constructing a confidence interval for the mean,the z distribution provides a result nearly identical to the t distribution when n is large.

Accepted Answer

A) True 
 B)False

Question 19

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.

Accepted Answer

We have sampled less than 5 percent of t

Question 20

To calculate the sample size needed for a survey to estimate a proportion,the population standard deviation σ must be known.

Accepted Answer

A) True 
 B)False

A sample of size 5 shows a mean of 45.2 and a sample standard deviation of 6.4.The standard error of the sample mean is approximately 2.86.

A 95 percent confidence interval constructed around p will be wider than a 90 percent confidence interval.

Sampling variation is not controllable by the statistician.

In constructing a 95 percent confidence interval,if you increase n to 4n,the width of your confidence interval will (assuming other things remain the same)be:

To estimate the average annual expenses of students on books and class materials a sample of size 36 is taken.The sample mean is $850 and the sample standard deviation is $54.A 99 percent confidence interval for the population mean is:

The confidence interval half-width when π = .50 is called the margin of error.

The Central Limit Theorem (CLT):

To estimate π,you typically need a sample size equal to at least 5 percent of your population.

The Central Limit Theorem guarantees an approximately normal sampling distribution when n is sufficiently large.

The width of a confidence interval for μ is not affected by:

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

A random sample of 16 ATM transactions at the Last National Bank of Flat Rock revealed a mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes.The width (in minutes)of the 95 percent confidence interval for the true mean transaction time is:

Read the news story below.Using the 95 percent confidence level,what sample size would be needed to estimate the true proportion of stores selling cigarettes to minors with an error of ± 3 percent? Explain carefully,showing all steps in your reasoning.

The efficiency of an estimator depends on the variance of the estimator's sampling distribution.

A higher confidence level leads to a narrower confidence interval,ceteris paribus.

The Central Limit Theorem says that a histogram of the sample means will have a bell shape,even if the population is skewed and the sample is small.

In constructing a confidence interval for the mean,the z distribution provides a result nearly identical to the t distribution when n is large.

To calculate the sample size needed for a survey to estimate a proportion,the population standard deviation σ must be known.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Multiple Regression

Time-Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

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Exam 8: Sampling Distributions and Estimation

A sample of size 5 shows a mean of 45.2 and a sample standard deviation of 6.4.The standard error of the sample mean is approximately 2.86.

A 95 percent confidence interval constructed around p will be wider than a 90 percent confidence interval.

Sampling variation is not controllable by the statistician.

In constructing a 95 percent confidence interval,if you increase n to 4n,the width of your confidence interval will (assuming other things remain the same)be:

To estimate the average annual expenses of students on books and class materials a sample of size 36 is taken.The sample mean is $850 and the sample standard deviation is $54.A 99 percent confidence interval for the population mean is:

The confidence interval half-width when π = .50 is called the margin of error.

The Central Limit Theorem (CLT):

To estimate π,you typically need a sample size equal to at least 5 percent of your population.

The Central Limit Theorem guarantees an approximately normal sampling distribution when n is sufficiently large.

The width of a confidence interval for μ is not affected by:

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

A random sample of 16 ATM transactions at the Last National Bank of Flat Rock revealed a mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes.The width (in minutes)of the 95 percent confidence interval for the true mean transaction time is:

Read the news story below.Using the 95 percent confidence level,what sample size would be needed to estimate the true proportion of stores selling cigarettes to minors with an error of ± 3 percent? Explain carefully,showing all steps in your reasoning.

The efficiency of an estimator depends on the variance of the estimator's sampling distribution.

A higher confidence level leads to a narrower confidence interval,ceteris paribus.

The Central Limit Theorem says that a histogram of the sample means will have a bell shape,even if the population is skewed and the sample is small.

In constructing a confidence interval for the mean,the z distribution provides a result nearly identical to the t distribution when n is large.

To calculate the sample size needed for a survey to estimate a proportion,the population standard deviation σ must be known.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Multiple Regression

Time-Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters