Question 1

How large a sample must be drawn to estimate the proportion of students who prefer statistics over mathematics, to within 0.02 with 95% confidence?

Accepted Answer

The answer of How large a sample must be drawn...

Question 2

At a given sample size and level of confidence, the smaller the population standard deviation $\sigma$ , the wider and thus the less precise the confidence interval estimate of $\mu$ is.

Accepted Answer

A) True 
 B)False

Question 3

A confidence interval is an interval estimate for which there is a specified degree of certainty that the actual value of the population parameter will fall within the interval.

Accepted Answer

A) True 
 B)False

Question 4

A random sample of size n has been selected from a normally distributed population whose standard deviation is s. In estimating an interval for the population mean, the t-distribution should be used instead of the z-test if: $\begin{array}{|l|l|}
\hline  A&\text { $ n \geq 30 $ and $ \sigma $ is known}\
\hline  B&\text {$ \sigma $ is unknown and estimated by $ s $, and the population is normal. }\
\hline  C&\text { Population is normal and $ \sigma $ is known.}\
\hline  D&\text {None of these choices are correct. }\
\hline 
\end{array}$

Accepted Answer

The answer of A random sample of size n has...

Question 5

Which of the following statistical distributions is used when estimating the population mean when the population variance is unknown? $\begin{array}{|l|l|}
\hline  A&\text {Student $ t $ distribution }\
\hline  B&\text { Standard normal distribution}\
\hline  C&\text { Chi-square distribution}\
\hline  D&\text {None of these choices are correct. }\
\hline 
\end{array}$

Accepted Answer

The answer of Which of the following statistical distributions is...

Question 6

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if both n - $\hat { p }$ and n - $\hat { q }$ are at least five ( $\hat { q }$ = 1 - $\hat { p }$ ).

Accepted Answer

A) True 
 B)False

Question 7

A survey of 100 retailers revealed that the mean after-tax profit was $80 000. Assuming that the population standard deviation is $15 000, determine the 95% confidence interval estimate of the mean after-tax profit for all retailers.

Accepted Answer

The answer of A survey of 100 retailers revealed that...

Question 8

In constructing a confidence interval for the population mean when the population variance is unknown, which of the following assumptions is required when using the following formula? $\bar { x } \pm t _ { a / 2 } \frac { s } { \sqrt { n } }$ $\begin{array}{|l|l|}
\hline  A&\text {The sample size is greater than 30 . }\
\hline  B&\text {The population variance is known. }\
\hline  C&\text { The population is normal.}\
\hline  D&\text {The sample is drawn from a positively skewed distribution. }\
\hline 
\end{array}$

Accepted Answer

The answer of In constructing a confidence interval for the...

Question 9

The range of a confidence interval is a measure of the expected sampling error.

Accepted Answer

A) True 
 B)False

Question 10

A confidence interval is defined as: $\begin{array}{|l|l|}
\hline  A&\text {a point estimate plus or minus a specific level of confidence. }\
\hline  B&\text { a lower and upper confidence limit associated with a specific level of confidence.}\
\hline  C&\text { an interval that has a $ 95 \% $ probability of containing the population parameter.}\
\hline  D&\text {a lower and upper confidence limit that has a $ 95 \% $ probability of containing the }\
&\text { population parameter.}\
\hline 
\end{array}$

Accepted Answer

The answer of A confidence interval is defined as: \(\begin{array}{|l|l|}
\hline...

Question 11

Which of the following assumptions must be true in order to use the formula $\bar { x } \pm z _ {\alpha / 2 } \sigma / \sqrt { n }$ to find a confidence interval estimate of the population mean? $\begin{array}{|l|l|}
\hline  A&\text {The population variance is known. }\
\hline  B&\text { The population mean is known.}\
\hline  C&\text { The population is normally distributed.}\
\hline  D&\text {The confidence level is greater than $ 90 \% $. }\
\hline 
\end{array}$

Accepted Answer

The answer of Which of the following assumptions must be...

Question 12

What is the width of a 99% confidence interval for the population proportion of people that own more than one mobile phone, if a random sample of 50 people was taken, and 10 of these had more than one mobile phone?

Accepted Answer

2(2.576 ×

Question 13

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion $\hat { p }$ , we: $\begin{array}{|l|l|}
\hline  A&\text {take another sample and estimate $ p $. }\
\hline  B&\text {take two more samples and find the average of their $ \hat{p} $ values. }\
\hline  C&\text {let $ \hat{p}=0.50 $. }\
\hline  D&\text {let $ \hat{p}=0.95 $. }\
\hline 
\end{array}$

Accepted Answer

The answer of In selecting the sample size to estimate...

Question 14

Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours.
Determine the 95% confidence interval estimate of the population mean, changing the sample size to 300.

Accepted Answer

6.3303 to

Question 15

Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

Accepted Answer

A) True 
 B)False

Question 16

A sample of 250 observations is to be selected at random from an infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion is: $\begin{array}{|l|l|}
\hline\text { A. } & 0.0274 . \
\hline \text { B. } & 0.50 . \
\hline \text { C. } & 0.0316 . \
\hline \text { D. } & 0.0548 . \
\hline
\end{array}$

Accepted Answer

The answer of A sample of 250 observations is to...

Question 17

In the formula $\bar { x } \pm z _ { \alpha / 2 } \sigma / \sqrt { n }$ , the $\alpha / 2$ refers to: $\begin{array}{|l|l|}
\hline  A&\text {the probability that the confidence interval will contain the populati on mean. }\
\hline  B&\text { the probability that the confidence interval will not contain the population mean. }\
\hline  C&\text {the area in the lower tail or upper tail of the sampling distribution of the sample mean.  }\
\hline  D&\text { the level of confidence.}\
\hline 
\end{array}$

Accepted Answer

The answer of In the formula \(\bar { x }...

Question 18

The upper limit of a confidence interval at the 99% level of confidence for the population proportion if a sample of size 100 had 40 successes is: $\begin{array}{|l|l|}
\hline\text { A. } & 0.3040 . \
\hline \text { B. } & 0.4047 . \
\hline \text { C. } & 0.4960 . \
\hline \text { D. } & 0.4806 . \
\hline
\end{array}$

Accepted Answer

The answer of The upper limit of a confidence interval...

Question 19

For a sample of size 30 taken from a normally distributed population with standard deviation equal to 5, a 95% confidence interval for the population mean would require the use of: $\begin{array}{|l|l|}
\hline\text { A. } & z=1.96 . \
\hline \text { B. } & z=1.645 . \
\hline \text { C. } & t=2.045 . \
\hline \text { D. } & t=1.699 . \
\hline
\end{array}$

Accepted Answer

The answer of For a sample of size 30 taken...

Question 20

The probability that a confidence interval includes the parameter of interest is either 1 or 0.

Accepted Answer

A) True 
 B)False

How large a sample must be drawn to estimate the proportion of students who prefer statistics over mathematics, to within 0.02 with 95% confidence?

At a given sample size and level of confidence, the smaller the population standard deviation $\sigma$ , the wider and thus the less precise the confidence interval estimate of $\mu$ is.

A confidence interval is an interval estimate for which there is a specified degree of certainty that the actual value of the population parameter will fall within the interval.

Which of the following statistical distributions is used when estimating the population mean when the population variance is unknown? A Student t distribution B Standard normal distribution C Chi-square distribution D None of these choices are correct.

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if both n - $\hat { p }$ and n - $\hat { q }$ are at least five ( $\hat { q }$ = 1 - $\hat { p }$ ).

A survey of 100 retailers revealed that the mean after-tax profit was $80 000. Assuming that the population standard deviation is $15 000, determine the 95% confidence interval estimate of the mean after-tax profit for all retailers.

The range of a confidence interval is a measure of the expected sampling error.

What is the width of a 99% confidence interval for the population proportion of people that own more than one mobile phone, if a random sample of 50 people was taken, and 10 of these had more than one mobile phone?

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion $\hat { p }$ , we: A take another sample and estimate p . B take two more samples and find the average of their values. C let =0.50 . D let =0.95 .

Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

A sample of 250 observations is to be selected at random from an infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion is: A. 0.0274. B. 0.50. C. 0.0316. D. 0.0548.

The upper limit of a confidence interval at the 99% level of confidence for the population proportion if a sample of size 100 had 40 successes is: A. 0.3040. B. 0.4047. C. 0.4960. D. 0.4806.

For a sample of size 30 taken from a normally distributed population with standard deviation equal to 5, a 95% confidence interval for the population mean would require the use of: A. z=1.96. B. z=1.645. C. t=2.045. D. t=1.699.

The probability that a confidence interval includes the parameter of interest is either 1 or 0.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 11: Estimation: Describing a Single Population

How large a sample must be drawn to estimate the proportion of students who prefer statistics over mathematics, to within 0.02 with 95% confidence?

At a given sample size and level of confidence, the smaller the population standard deviation σ\sigmaσ , the wider and thus the less precise the confidence interval estimate of μ\muμ is.

A confidence interval is an interval estimate for which there is a specified degree of certainty that the actual value of the population parameter will fall within the interval.

Which of the following statistical distributions is used when estimating the population mean when the population variance is unknown? A Student t distribution B Standard normal distribution C Chi-square distribution D None of these choices are correct.

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if both n - p^\hat { p }p^​ and n - q^\hat { q }q^​ are at least five ( q^\hat { q }q^​ = 1 - p^\hat { p }p^​ ).

A survey of 100 retailers revealed that the mean after-tax profit was $80 000. Assuming that the population standard deviation is $15 000, determine the 95% confidence interval estimate of the mean after-tax profit for all retailers.

The range of a confidence interval is a measure of the expected sampling error.

What is the width of a 99% confidence interval for the population proportion of people that own more than one mobile phone, if a random sample of 50 people was taken, and 10 of these had more than one mobile phone?

Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

A sample of 250 observations is to be selected at random from an infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion is: A. 0.0274. B. 0.50. C. 0.0316. D. 0.0548.

The upper limit of a confidence interval at the 99% level of confidence for the population proportion if a sample of size 100 had 40 successes is: A. 0.3040. B. 0.4047. C. 0.4960. D. 0.4806.

For a sample of size 30 taken from a normally distributed population with standard deviation equal to 5, a 95% confidence interval for the population mean would require the use of: A. z=1.96. B. z=1.645. C. t=2.045. D. t=1.699.

The probability that a confidence interval includes the parameter of interest is either 1 or 0.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

At a given sample size and level of confidence, the smaller the population standard deviation $\sigma$ , the wider and thus the less precise the confidence interval estimate of $\mu$ is.

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if both n - $\hat { p }$ and n - $\hat { q }$ are at least five ( $\hat { q }$ = 1 - $\hat { p }$ ).