A 95% confidence interval estimate for a population mean $\mu$ is determined to be 43.78 to 52.19. If the confidence level is decreased to 90%, the confidence interval$\mu$ : $\begin{array}{|l|l|} \hline A&\text {becomes wider. }\\ \hline B&\text {remains the same. }\\ \hline C&\text {becomes narrower. }\\ \hline D&\text {None of these choices are correct. }\\ \hline \end{array}$

The answer of A 95% confidence interval estimate for a...

The sample variance $s ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ when the denominator of $s ^ { 2 }$ is: $\begin{array}{|l|l|} \hline\text { A. } & n . \\ \hline \text { B. } & n-1 \\ \hline \text { C. } & \sqrt{n } \\ \hline \text { D. } & n+1 \\ \hline \end{array}$

The answer of The sample variance \(s ^ { 2...

A robust estimator is one that: $\begin{array}{|l|l|} \hline A&\text {is unbiased and symmetrical about zero. }\\ \hline B&\text {is consistent and is also mound-shaped. }\\ \hline C&\text { is efficient and less spread out.}\\ \hline D&\text { is not sensitive to moderate departure from the assumption of normality in the population.}\\ \hline \end{array}$

The answer of A robust estimator is one that: \(\begin{array}{|l|l|} \hline...

Exam 11: Estimation: Describing a Single Population

A 95% confidence interval estimate for a population mean $\mu$ is determined to be 43.78 to 52.19. If the confidence level is decreased to 90%, the confidence interval $\mu$ : A becomes wider. B remains the same. C becomes narrower. D None of these choices are correct.

(Short Answer)

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Question 21

It is possible to construct a confidence interval estimate of the population mean if the population variance is unknown.

(True/False)

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Question 22

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

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Question 23

A simple random sample of 100 observations is taken from a population. Assume that the population proportion p = 0.5. a. What is the expected value of the sample proportion $\hat { p }$ ? b. What is the standard error of the sample proportion $\hat { p }$ ?

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Question 24

Which of the following statements is (are) correct? A The sample mean is a biased estimat or of the population mean. B The sample proportion is an unbiased estimat or of the population proportion. C The sample mean is not a consistent estimator. D All of these choices are correct.

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Question 25

How large a sample should be taken to estimate a population proportion to within 0.01 with 90% confidence if the proportion is known to be around 5%?

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Question 26

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 population standard deviation to 2.

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Question 27

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 90% confidence interval estimate of the population mean.

(Short Answer)

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Question 28

The sample variance $s ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ when the denominator of $s ^ { 2 }$ is: A. n. B. n-1 C. D. n+1

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Question 29

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had $\sigma$ equaled 20, the interval estimate would have been: A. 60.92\pm2.14. B. 50.92\pm12.14 C. 101.84\pm4.28 D. 50.92\pm4.28.

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Question 30

Suppose that a 90% confidence interval for $\mu$ is given by $\bar { x } \pm 0.75$ . This notation means that we are 90% confident that $\mu$ falls between $\bar { x } - 0.75$ and $\bar { x } + 0.75$ .

(True/False)

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Question 31

A random sample of 10 university students was surveyed to determine the amount of time they spent weekly using a personal computer. The times (in hours) were: 13 14 5 6 8 10 7 12 15 3 If the times are normally distributed with a standard deviation of 5.2 hours, estimate with 90% confidence the mean weekly time spent using a personal computer for all university students.

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Question 32

As a manufacturer of golf clubs, a major corporation wants to estimate the proportion of golfers who are right-handed. How many golfers must be surveyed if they want to be within 0.02 with a 95% confidence level: a. assuming that there is no information available that could be used as an estimate of p? b. assuming that the manufacturer has an estimate of p obtained from a previous study that suggests that 75% of golfers are right-handed?

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Question 33

The width of a confidence interval increases as the level of significance increases.

(True/False)

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Question 34

A random sample of 64 observations has a mean of 30. The population variance is assumed to be 9. The 85.3% confidence interval estimate for the population mean (to the third decimal place) is: A. 28.369\pm31.631. B. 29.456\pm30.544. C. 28.560\pm31.440. D. 29.383\pm30.617.

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Question 35

The sample mean is an unbiased estimator of the population mean $\mu$ , and (when sampling from a normal population) the sample median is also an unbiased estimator of $\mu$ . However, the sample mean is relatively more efficient than the sample median.

(True/False)

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Question 36

The sample standard deviation is an unbiased estimator of the population standard deviation.

(True/False)

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Question 37

After you calculate the sample size needed to estimate a population proportion to within 0.05, your statistics lecturer tells you the maximum allowable error must be reduced to just 0.025. If the original calculation led to a sample size of 400, the sample size will now have to be: A. 800. B. 200. C. 4000. D. 1600

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Question 38

The population proportion of voters in favour of a particular political candidate is being estimated with a confidence interval. A random sample of 55 voters is taken, and 28 are found to be in favour. Find and interpret a 90% confidence interval for the population proportion of people in favour of this political candidate.

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Question 39

A robust estimator is one that: A is unbiased and symmetrical about zero. B is consistent and is also mound-shaped. C is efficient and less spread out. D is not sensitive to moderate departure from the assumption of normality in the population.

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Question 40

A 95% confidence interval estimate for a population mean $\mu$ is determined to be 43.78 to 52.19. If the confidence level is decreased to 90%, the confidence interval $\mu$ : A becomes wider. B remains the same. C becomes narrower. D None of these choices are correct.

It is possible to construct a confidence interval estimate of the population mean if the population variance is unknown.

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

A simple random sample of 100 observations is taken from a population. Assume that the population proportion p = 0.5. a. What is the expected value of the sample proportion $\hat { p }$ ? b. What is the standard error of the sample proportion $\hat { p }$ ?

Which of the following statements is (are) correct? A The sample mean is a biased estimat or of the population mean. B The sample proportion is an unbiased estimat or of the population proportion. C The sample mean is not a consistent estimator. D All of these choices are correct.

How large a sample should be taken to estimate a population proportion to within 0.01 with 90% confidence if the proportion is known to be around 5%?

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 90% confidence interval estimate of the population mean.

The sample variance $s ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ when the denominator of $s ^ { 2 }$ is: A. n. B. n-1 C. D. n+1

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had $\sigma$ equaled 20, the interval estimate would have been: A. 60.92\pm2.14. B. 50.92\pm12.14 C. 101.84\pm4.28 D. 50.92\pm4.28.

Suppose that a 90% confidence interval for $\mu$ is given by $\bar { x } \pm 0.75$ . This notation means that we are 90% confident that $\mu$ falls between $\bar { x } - 0.75$ and $\bar { x } + 0.75$ .

The width of a confidence interval increases as the level of significance increases.

A random sample of 64 observations has a mean of 30. The population variance is assumed to be 9. The 85.3% confidence interval estimate for the population mean (to the third decimal place) is: A. 28.369\pm31.631. B. 29.456\pm30.544. C. 28.560\pm31.440. D. 29.383\pm30.617.

The sample mean is an unbiased estimator of the population mean $\mu$ , and (when sampling from a normal population) the sample median is also an unbiased estimator of $\mu$ . However, the sample mean is relatively more efficient than the sample median.

The sample standard deviation is an unbiased estimator of the population standard deviation.

A robust estimator is one that: A is unbiased and symmetrical about zero. B is consistent and is also mound-shaped. C is efficient and less spread out. D is not sensitive to moderate departure from the assumption of normality in the population.

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

A 95% confidence interval estimate for a population mean μ\muμ is determined to be 43.78 to 52.19. If the confidence level is decreased to 90%, the confidence interval μ\muμ : A becomes wider. B remains the same. C becomes narrower. D None of these choices are correct.

It is possible to construct a confidence interval estimate of the population mean if the population variance is unknown.

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

A simple random sample of 100 observations is taken from a population. Assume that the population proportion p = 0.5. a. What is the expected value of the sample proportion p^\hat { p }p^​ ? b. What is the standard error of the sample proportion p^\hat { p }p^​ ?

Which of the following statements is (are) correct? A The sample mean is a biased estimat or of the population mean. B The sample proportion is an unbiased estimat or of the population proportion. C The sample mean is not a consistent estimator. D All of these choices are correct.

How large a sample should be taken to estimate a population proportion to within 0.01 with 90% confidence if the proportion is known to be around 5%?

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 90% confidence interval estimate of the population mean.

The sample variance s2s ^ { 2 }s2 is an unbiased estimator of the population variance σ2\sigma ^ { 2 }σ2 when the denominator of s2s ^ { 2 }s2 is: A. n. B. n-1 C. D. n+1

In developing an interval estimate for a population mean, the population standard deviation σ\sigmaσ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had σ\sigmaσ equaled 20, the interval estimate would have been: A. 60.92\pm2.14. B. 50.92\pm12.14 C. 101.84\pm4.28 D. 50.92\pm4.28.

Suppose that a 90% confidence interval for μ\muμ is given by xˉ±0.75\bar { x } \pm 0.75xˉ±0.75 . This notation means that we are 90% confident that μ\muμ falls between xˉ−0.75\bar { x } - 0.75xˉ−0.75 and xˉ+0.75\bar { x } + 0.75xˉ+0.75 .

The width of a confidence interval increases as the level of significance increases.

A random sample of 64 observations has a mean of 30. The population variance is assumed to be 9. The 85.3% confidence interval estimate for the population mean (to the third decimal place) is: A. 28.369\pm31.631. B. 29.456\pm30.544. C. 28.560\pm31.440. D. 29.383\pm30.617.

The sample mean is an unbiased estimator of the population mean μ\muμ , and (when sampling from a normal population) the sample median is also an unbiased estimator of μ\muμ . However, the sample mean is relatively more efficient than the sample median.

The sample standard deviation is an unbiased estimator of the population standard deviation.

A robust estimator is one that: A is unbiased and symmetrical about zero. B is consistent and is also mound-shaped. C is efficient and less spread out. D is not sensitive to moderate departure from the assumption of normality in the population.

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

A 95% confidence interval estimate for a population mean $\mu$ is determined to be 43.78 to 52.19. If the confidence level is decreased to 90%, the confidence interval $\mu$ : A becomes wider. B remains the same. C becomes narrower. D None of these choices are correct.

A simple random sample of 100 observations is taken from a population. Assume that the population proportion p = 0.5. a. What is the expected value of the sample proportion $\hat { p }$ ? b. What is the standard error of the sample proportion $\hat { p }$ ?

The sample variance $s ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ when the denominator of $s ^ { 2 }$ is: A. n. B. n-1 C. D. n+1

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had $\sigma$ equaled 20, the interval estimate would have been: A. 60.92\pm2.14. B. 50.92\pm12.14 C. 101.84\pm4.28 D. 50.92\pm4.28.

Suppose that a 90% confidence interval for $\mu$ is given by $\bar { x } \pm 0.75$ . This notation means that we are 90% confident that $\mu$ falls between $\bar { x } - 0.75$ and $\bar { x } + 0.75$ .

The sample mean is an unbiased estimator of the population mean $\mu$ , and (when sampling from a normal population) the sample median is also an unbiased estimator of $\mu$ . However, the sample mean is relatively more efficient than the sample median.