The following table gives the number of pets owned for a population of four families. \[\begin{array} { | l | c | c | c | c | } \hline \text { Family } & \text { A } & \text { B } & \text { C } & \text { D } \\ \hline \text { Number of pets owned } & 2 & 1 & 4 & 3 \\ \hline \end{array}\] List all possible samples of two families that can be selected without replacement from this population, and compute the sample mean $\bar { x }$ for each sample.

The answer of The following table gives the number of...

The finite population correction factor should not be used when: $\begin{array}{|l|l|} \hline A&\text { we are sampling from an infinite population.}\\ \hline B&\text { we are sampling from a finite population.}\\ \hline C&\text { sample size is greater than \( 1 \% $ of the population size. }\\ \hline D&\text { None of these choices are correct.}\\ \hline \end{array}\)

The answer of The finite population correction factor should not...

Which of the following best describes the Central Limit Theorem? $\begin{array}{|l|l|} \hline A&\text { If the distribution of a random variable is non-normal, the sampling distribution of the sample}\\ &\text {mean will be approximately normal for samples \( n \geq 30 $. }\\ \hline B&\text {The sample mean is close to 0.50 . }\\ \hline C&\text {The underlying population is normal. }\\ \hline D&\text { All of these choices are correct.}\\ \hline \end{array}\)

The answer of Which of the following best describes the...

Exam 10: Sampling Distributions

Assume that the time needed by a worker to perform a maintenance operation is normally distributed, with a mean of 60 minutes and a standard deviation of 6 minutes. What is the probability that the average time needed by a sample of 5 workers to perform the maintenance is between 63 and 68 minutes?

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Question 1

Correct Answer:

Verified

0.13.

A sample of size 50 is to be taken from an infinite population whose mean and standard deviation are 52 and 20, respectively. The probability that the sample mean will be larger than 49 is: A. 0.4452. B. 0.9452. C. 0.8554. D. 0.3554.

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Question 2

Correct Answer:

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C

If all possible samples of size n are drawn from an infinite population with mean $\mu$ and standard deviation $\sigma$ , then the standard error of the sample mean is inversely proportional to: A. \mu. B. \sigma. C. n D.

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Question 3

Correct Answer:

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D

A sample of 30 observations is drawn from a normal population with mean of 750 and a standard deviation of 300. Suppose the population size is 600. a. Find the expected value of the sample mean $\bar { X }$ . b. Find the standard error of the sample mean $\bar { X }$ . c. Find P( $\bar { X }$ > 790). d. Find P( $\bar { X }$ < 650). e. Find P(760 < $\bar { X }$ < 810).

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Question 4

A sample of size 400 is drawn from a population whose mean and variance are 5000 and 10 000, respectively. Find the following probabilities. a. P( $\bar { X }$ < 4,990). b. P(4995 < $\bar { X }$ < 5010). c. P( $\bar { X }$ = 5000).

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Question 5

The sampling distribution of the sample proportion is always normally distributed.

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Question 6

The standard error of the mean is the standard deviation of the sampling distribution of $\bar { X }$ .

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Question 7

Using the following sampling distribution, directly recalculate the mean and standard deviation of $\bar { X }$ . 1.5 2.0 2.5 3.0 3.5 p() 1/6 1/6 1/6 1/6 1/6

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Question 8

The sampling distribution of the sample proportion is approximately normal provided that np ≥ 5 and nq ≥ 5

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Question 9

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean $\bar { X }$ is referred to as the normal distribution.

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Question 10

A sample of size 70 is selected at random from a finite population. If the finite population correction factor is 0.808, the population size (rounded to the nearest integer) must be 200.

(True/False)

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Question 11

Consider an infinite population with a mean of 160 and a standard deviation of 25. A random sample of size 64 is taken from this population. The standard deviation of the sample mean equals: A. 12.649 B. 25.0. C. 2.56. D. 3.125.

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Question 12

A population that consists of 250 items has a mean of 37 and a standard deviation of 13. A sample of size 5 is taken at random from this population. The standard error of the sample mean equals (up to three decimal places): A. 1.838. B. 1.648. C. 0.822 D. 2.715.

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Question 13

A sample of size n is selected at random from an infinite population. As n increases the standard error of the sample mean decreases.

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Question 14

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. What is the probability that the mean height of a random sample of 30 women is smaller than 162 centimetres?

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Question 15

The following table gives the number of pets owned for a population of four families. Family A B C D Number of pets owned 2 1 4 3 List all possible samples of two families that can be selected without replacement from this population, and compute the sample mean $\bar { x }$ for each sample.

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Question 16

An auditor knows from past history that the average accounts receivable for a company is $521.72, with a standard deviation of $584.64. If the auditor takes a simple random sample of 100 accounts, what is the probability that the mean of the sample will be within $120 of the population mean?

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Question 17

The finite population correction factor should not be used when: A we are sampling from an infinite population. B we are sampling from a finite population. C sample size is greater than 1 \% of the population size. D None of these choices are correct.

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Question 18

Which of the following best describes the Central Limit Theorem? A If the distribution of a random variable is non-normal, the sampling distribution of the sample mean will be approximately normal for samples n \geq 30 . B The sample mean is close to 0.50 . C The underlying population is normal. D All of these choices are correct.

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Question 19

The central limit theorem is basic to the concept of statistical inference, because it permits us to draw conclusions about the population based strictly on sample data, and without having any knowledge about the distribution of the underlying population.

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Question 20

Exam 10: Sampling Distributions

Assume that the time needed by a worker to perform a maintenance operation is normally distributed, with a mean of 60 minutes and a standard deviation of 6 minutes. What is the probability that the average time needed by a sample of 5 workers to perform the maintenance is between 63 and 68 minutes?

A sample of size 50 is to be taken from an infinite population whose mean and standard deviation are 52 and 20, respectively. The probability that the sample mean will be larger than 49 is: A. 0.4452. B. 0.9452. C. 0.8554. D. 0.3554.

If all possible samples of size n are drawn from an infinite population with mean μ\muμ and standard deviation σ\sigmaσ , then the standard error of the sample mean is inversely proportional to: A. \mu. B. \sigma. C. n D.

A sample of size 400 is drawn from a population whose mean and variance are 5000 and 10 000, respectively. Find the following probabilities. a. P( Xˉ\bar { X }Xˉ < 4,990). b. P(4995 < Xˉ\bar { X }Xˉ < 5010). c. P( Xˉ\bar { X }Xˉ = 5000).

The sampling distribution of the sample proportion is always normally distributed.

The standard error of the mean is the standard deviation of the sampling distribution of Xˉ\bar { X }Xˉ .

Using the following sampling distribution, directly recalculate the mean and standard deviation of Xˉ\bar { X }Xˉ . 1.5 2.0 2.5 3.0 3.5 p() 1/6 1/6 1/6 1/6 1/6

The sampling distribution of the sample proportion is approximately normal provided that np ≥ 5 and nq ≥ 5

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean Xˉ\bar { X }Xˉ is referred to as the normal distribution.

A sample of size 70 is selected at random from a finite population. If the finite population correction factor is 0.808, the population size (rounded to the nearest integer) must be 200.

Consider an infinite population with a mean of 160 and a standard deviation of 25. A random sample of size 64 is taken from this population. The standard deviation of the sample mean equals: A. 12.649 B. 25.0. C. 2.56. D. 3.125.

A population that consists of 250 items has a mean of 37 and a standard deviation of 13. A sample of size 5 is taken at random from this population. The standard error of the sample mean equals (up to three decimal places): A. 1.838. B. 1.648. C. 0.822 D. 2.715.

A sample of size n is selected at random from an infinite population. As n increases the standard error of the sample mean decreases.

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. What is the probability that the mean height of a random sample of 30 women is smaller than 162 centimetres?

The following table gives the number of pets owned for a population of four families. Family A B C D Number of pets owned 2 1 4 3 List all possible samples of two families that can be selected without replacement from this population, and compute the sample mean xˉ\bar { x }xˉ for each sample.

An auditor knows from past history that the average accounts receivable for a company is $521.72, with a standard deviation of $584.64. If the auditor takes a simple random sample of 100 accounts, what is the probability that the mean of the sample will be within $120 of the population mean?

The finite population correction factor should not be used when: A we are sampling from an infinite population. B we are sampling from a finite population. C sample size is greater than 1 \% of the population size. D None of these choices are correct.

The central limit theorem is basic to the concept of statistical inference, because it permits us to draw conclusions about the population based strictly on sample data, and without having any knowledge about the distribution of the underlying 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

Estimation: Describing a Single Population

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

If all possible samples of size n are drawn from an infinite population with mean $\mu$ and standard deviation $\sigma$ , then the standard error of the sample mean is inversely proportional to: A. \mu. B. \sigma. C. n D.

A sample of size 400 is drawn from a population whose mean and variance are 5000 and 10 000, respectively. Find the following probabilities. a. P( $\bar { X }$ < 4,990). b. P(4995 < $\bar { X }$ < 5010). c. P( $\bar { X }$ = 5000).

The standard error of the mean is the standard deviation of the sampling distribution of $\bar { X }$ .

Using the following sampling distribution, directly recalculate the mean and standard deviation of $\bar { X }$ . 1.5 2.0 2.5 3.0 3.5 p() 1/6 1/6 1/6 1/6 1/6

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean $\bar { X }$ is referred to as the normal distribution.

The following table gives the number of pets owned for a population of four families. Family A B C D Number of pets owned 2 1 4 3 List all possible samples of two families that can be selected without replacement from this population, and compute the sample mean $\bar { x }$ for each sample.