Exam 11: Estimation: Describing a Single Population

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should be used if you wish to estimate the population mean to within 5 units?

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Question 21

The sample mean $\hat x$ is a consistent estimator of the population mean $\mu$ .

(True/False)

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Question 22

An interval estimate is a range of values within which the actual value of a population parameter $\mu$ falls.

(True/False)

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Question 23

In developing an interval estimate at 87.4% for a population mean, the value of z to use is:

(Multiple Choice)

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Question 24

If the standard error of the sampling distribution of the sample proportion is 0.0337 for samples of size 200, then the population proportion must be:

(Multiple Choice)

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Question 25

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.

(True/False)

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Question 26

The smaller the level of confidence used in constructing a confidence interval estimate of the population mean, the:

(Multiple Choice)

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Question 27

A random sample of size 20 taken from a normally distributed population resulted in a sample variance of 32. The lower limit of a 90% confidence interval for the population variance would be:

(Multiple Choice)

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Question 28

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:

(Multiple Choice)

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Question 29

The standard error of the sampling distribution of the sample proportion $\hat { p }$ , when the sample size n = 100 and the population proportion p = 0.30, is 0.0021.

(True/False)

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Question 30

The student t-distribution approaches the normal distribution as the:

(Multiple Choice)

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Question 31

Which of the following is not a part of the formula for constructing a confidence interval estimate of the population mean?

(Multiple Choice)

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Question 32

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 8. The interval estimate was 50.0 ± 2.50. Had $\sigma$ equalled 16, the interval estimate would have been 100 ± 5.0.

(True/False)

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Question 33

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

(True/False)

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Question 34

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. What happens to the width of the confidence interval estimate when each of the following things happens? a. The confidence level increases. b. The confidence level decreases. c. The sample size increases. d. The sample size decreases. e. The value of the population standard deviation increases. f. The value of the population standard deviation decreases. g. The value of the sample mean increases. h. The value of the sample mean decreases.

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Question 35

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 99% confidence interval estimate of the population mean.

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Question 36

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

(True/False)

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Question 37

A 95% confidence interval estimate for a population mean $\mu$ is determined to be 75 to 85. If the confidence level is reduced to 80%, the confidence interval for $\mu$ becomes narrower.

(True/False)

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Question 38

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

(True/False)

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Question 39

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

(True/False)

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Question 40

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Exam 11: Estimation: Describing a Single Population

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should be used if you wish to estimate the population mean to within 5 units?

The sample mean x^\hat xx^ is a consistent estimator of the population mean μ\muμ .

An interval estimate is a range of values within which the actual value of a population parameter μ\muμ falls.

In developing an interval estimate at 87.4% for a population mean, the value of z to use is:

If the standard error of the sampling distribution of the sample proportion is 0.0337 for samples of size 200, then the population proportion must be:

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.

The smaller the level of confidence used in constructing a confidence interval estimate of the population mean, the:

A random sample of size 20 taken from a normally distributed population resulted in a sample variance of 32. The lower limit of a 90% confidence interval for the population variance would be:

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 p^\hat { p }p^​ , we:

The standard error of the sampling distribution of the sample proportion p^\hat { p }p^​ , when the sample size n = 100 and the population proportion p = 0.30, is 0.0021.

The student t-distribution approaches the normal distribution as the:

Which of the following is not a part of the formula for constructing a confidence interval estimate of the population mean?

In developing an interval estimate for a population mean, the population standard deviation σ\sigmaσ was assumed to be 8. The interval estimate was 50.0 ± 2.50. Had σ\sigmaσ equalled 16, the interval estimate would have been 100 ± 5.0.

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 n - 1.

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 99% confidence interval estimate of the population mean.

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

A 95% confidence interval estimate for a population mean μ\muμ is determined to be 75 to 85. If the confidence level is reduced to 80%, the confidence interval for μ\muμ becomes narrower.

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

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

The sample mean $\hat x$ is a consistent estimator of the population mean $\mu$ .

An interval estimate is a range of values within which the actual value of a population parameter $\mu$ falls.

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:

The standard error of the sampling distribution of the sample proportion $\hat { p }$ , when the sample size n = 100 and the population proportion p = 0.30, is 0.0021.

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 8. The interval estimate was 50.0 ± 2.50. Had $\sigma$ equalled 16, the interval estimate would have been 100 ± 5.0.

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

A 95% confidence interval estimate for a population mean $\mu$ is determined to be 75 to 85. If the confidence level is reduced to 80%, the confidence interval for $\mu$ becomes narrower.