Exam 10: Estimation: Describing a Single Population

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:

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(Multiple Choice)

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Question 1

Correct Answer:

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The use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p requires that:

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Question 2

Correct Answer:

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

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(True/False)

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Question 3

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True

If the standard error of the sampling distribution of the sample proportion is 0.0229 for samples of size 400, then the population proportion must be either:

(Multiple Choice)

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Question 4

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

(True/False)

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Question 5

Which of the following is the width of the confidence interval for the population mean?

(Multiple Choice)

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Question 6

A sample of size 200 is to be taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion will be greater than 0.58 is:

(Multiple Choice)

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Question 7

When constructing a confidence interval estimate of ? , doubling the sample size n reduces the width %of the interval by half.

(True/False)

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Question 8

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.

(Short Answer)

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Question 9

Which of the following statements are correct?

(Multiple Choice)

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Question 10

In the formula $\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )$ , the subscript $\alpha / 2$ refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

(True/False)

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Question 11

The width of a confidence interval estimate of the population mean widens when the:

(Multiple Choice)

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Question 12

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 mean to 8.5 hours.

(Short Answer)

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Question 13

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 you use?

(Short Answer)

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Question 14

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 15

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 16

How large a sample of state employees should be taken if we want to estimate with 98% confidence the mean salary to within $2000. The population standard deviation is assumed to be $10 500.

(Short Answer)

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Question 17

If the Student t distribution is incorrectly used instead of the Standard normal distribution when finding the confidence interval for the population mean, and the population variance was known, what will happen to the width of the confidence interval?

(Multiple Choice)

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Question 18

The larger the level of confidence used in constructing a confidence interval, the wider the confidence interval.

(True/False)

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Question 19

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 you use with a 99% confidence level?

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Question 20

Showing 1 - 20 of 125

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:

The use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p requires that:

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

If the standard error of the sampling distribution of the sample proportion is 0.0229 for samples of size 400, then the population proportion must be either:

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

Which of the following is the width of the confidence interval for the population mean?

A sample of size 200 is to be taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion will be greater than 0.58 is:

When constructing a confidence interval estimate of ? , doubling the sample size n reduces the width %of the interval by half.

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.

Which of the following statements are correct?

In the formula $\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )$ , the subscript $\alpha / 2$ refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

The width of a confidence interval estimate of the population mean widens when the:

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 you use?

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 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.

How large a sample of state employees should be taken if we want to estimate with 98% confidence the mean salary to within $2000. The population standard deviation is assumed to be $10 500.

If the Student t distribution is incorrectly used instead of the Standard normal distribution when finding the confidence interval for the population mean, and the population variance was known, what will happen to the width of the confidence interval?

The larger the level of confidence used in constructing a confidence interval, the wider the confidence interval.

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 you use with a 99% confidence level?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

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Exam 10: Estimation: Describing a Single Population

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:

The use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p requires that:

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

If the standard error of the sampling distribution of the sample proportion is 0.0229 for samples of size 400, then the population proportion must be either:

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

Which of the following is the width of the confidence interval for the population mean?

A sample of size 200 is to be taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion will be greater than 0.58 is:

When constructing a confidence interval estimate of ? , doubling the sample size n reduces the width %of the interval by half.

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.

Which of the following statements are correct?

In the formula Xˉ±za/2(σ/n)\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )Xˉ±za/2​(σ/n​) , the subscript α/2\alpha / 2α/2 refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

The width of a confidence interval estimate of the population mean widens when the:

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 you use?

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.

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.

How large a sample of state employees should be taken if we want to estimate with 98% confidence the mean salary to within $2000. The population standard deviation is assumed to be $10 500.

If the Student t distribution is incorrectly used instead of the Standard normal distribution when finding the confidence interval for the population mean, and the population variance was known, what will happen to the width of the confidence interval?

The larger the level of confidence used in constructing a confidence interval, the wider the confidence interval.

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 you use with a 99% confidence level?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

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

In the formula $\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )$ , the subscript $\alpha / 2$ refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

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