Exam 7: Probability and Samples: the Distribution of Sample Means

A sample of n = 4 scores is selected from a population with µ = 30 and s = 8.The probability of obtaining a sample mean greater than 34 is equal to the probability of obtaining a z-score greater than z = 2.00 from a normal distribution.

(True/False)

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Question 41

For a normal population with µ = 100 and σ = 20: a. What is the probability of obtaining a sample mean greater than 110 for a sample of n = 4 scores? b. What is the probability of obtaining a sample mean greater than 110 for a sample of n = 16 scores? c. For a sample of n = 25 scores, what is the probability that the sample mean will be within 5 points of the population mean? In other words, what is p(95 < M < 105)?

(Short Answer)

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Question 42

The law of large numbers states that the larger the sample size (n),the more probable it is that the sample mean will be close to the population mean..

(True/False)

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Question 43

A random sample of n = 4 scores is selected from a population.Which of the following distributions will definitively be normal?

(Multiple Choice)

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Question 44

A mathematical proposition known as the central limit theorem provides a precise description of the distribution that would be obtained if you selected every possible sample,calculated every sample mean,and constructed the distribution of the sample mean.

(True/False)

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Question 45

If the standard deviation for a population increases,the standard error for sample means from the population will also increase.

(True/False)

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Question 46

A sample of n = 4 scores is selected from a population with µ = 70 and s = 10.The probability of obtaining a sample mean greater than 65 is p = 0.8413.

(True/False)

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Question 47

What happens to the expected value of M as sample size increases?

(Multiple Choice)

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Question 48

A random sample of n = 4 scores is obtained from a normal population with µ = 20 and σ = 4.What is the probability that the sample mean will be greater than M = 22?

(Multiple Choice)

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Question 49

The smallest possible standard error is obtained when a small sample is taken from a population with a small standard deviation.

(True/False)

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Question 50

A researcher obtained M = 27 for a sample of n = 36 scores selected from a population with µ = 30 and s = 18.This sample mean corresponds to a z-score of z = -1.00.

(True/False)

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Question 51

For a population with µ = 80 and σ = 20,the distribution of sample means based on n = 16 will have an expected value of and a standard error of .

(Multiple Choice)

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Question 52

A sample of n = 9 scores is obtained from a population with μ = 70 and σ = 18.If the sample mean is M = 76,then what is the z-score for the sample mean?

(Multiple Choice)

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Question 53

If random samples,each with n = 36 scores,are selected from a normal population with µ = 80 and σ = 18,how much difference,on average,should there be between a sample mean and the population mean?

(Multiple Choice)

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Question 54

A sample of n = 4 scores is selected from a population with μ = 50 and σ = 12.If the sample mean is M = 56,what is the z-score for this sample mean?

(Multiple Choice)

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Question 55

The distribution of sample means is the collection of sample means for all the possible random samples of a particular size (n)that can be obtained from a population.

(True/False)

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Question 56

The mean for a sample of n = 4 scores has a standard error σ_M = 5 points.This sample was selected from a population with a standard deviation of σ = 20.

(True/False)

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Question 57

A sample is obtained from a population with s = 20.If the sample mean has a standard error of 5 points,then the sample size is n = 4.

(True/False)

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Question 58

The distribution of sample means ____.

(Multiple Choice)

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Question 59

A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 6.What is the probability that the sample mean will be greater than M = 43?

(Multiple Choice)

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Question 60

Showing 41 - 60 of 77

A sample of n = 4 scores is selected from a population with µ = 30 and s = 8.The probability of obtaining a sample mean greater than 34 is equal to the probability of obtaining a z-score greater than z = 2.00 from a normal distribution.

The law of large numbers states that the larger the sample size (n),the more probable it is that the sample mean will be close to the population mean..

A random sample of n = 4 scores is selected from a population.Which of the following distributions will definitively be normal?

A mathematical proposition known as the central limit theorem provides a precise description of the distribution that would be obtained if you selected every possible sample,calculated every sample mean,and constructed the distribution of the sample mean.

If the standard deviation for a population increases,the standard error for sample means from the population will also increase.

A sample of n = 4 scores is selected from a population with µ = 70 and s = 10.The probability of obtaining a sample mean greater than 65 is p = 0.8413.

What happens to the expected value of M as sample size increases?

A random sample of n = 4 scores is obtained from a normal population with µ = 20 and σ = 4.What is the probability that the sample mean will be greater than M = 22?

The smallest possible standard error is obtained when a small sample is taken from a population with a small standard deviation.

A researcher obtained M = 27 for a sample of n = 36 scores selected from a population with µ = 30 and s = 18.This sample mean corresponds to a z-score of z = -1.00.

For a population with µ = 80 and σ = 20,the distribution of sample means based on n = 16 will have an expected value of and a standard error of .

A sample of n = 9 scores is obtained from a population with μ = 70 and σ = 18.If the sample mean is M = 76,then what is the z-score for the sample mean?

If random samples,each with n = 36 scores,are selected from a normal population with µ = 80 and σ = 18,how much difference,on average,should there be between a sample mean and the population mean?

A sample of n = 4 scores is selected from a population with μ = 50 and σ = 12.If the sample mean is M = 56,what is the z-score for this sample mean?

The distribution of sample means is the collection of sample means for all the possible random samples of a particular size (n)that can be obtained from a population.

The mean for a sample of n = 4 scores has a standard error σ_M = 5 points.This sample was selected from a population with a standard deviation of σ = 20.

A sample is obtained from a population with s = 20.If the sample mean has a standard error of 5 points,then the sample size is n = 4.

The distribution of sample means ____.

A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 6.What is the probability that the sample mean will be greater than M = 43?

Introduction to Statistics

Frequency Distributions

Central Tendency

Variability

Z-Scores: Location of Scores and Standardized Distributions

Probability

Introduction to Hypothesis Testing

Introduction to the T Statistic

The T Test for Two Independent Samples

The T Test for Two Related Samples

Introduction to Analysis of Variance

Repeated-Measures Analysis of Variance Anova

Two-Factor Analysis of Variance Independent Measures

Correlation

Introduction to Regression

The Chi-Square Statistic: Tests for Goodness of Fit and Independence

The Binomial Test

Filters

Exam 7: Probability and Samples: the Distribution of Sample Means

A sample of n = 4 scores is selected from a population with µ = 30 and s = 8.The probability of obtaining a sample mean greater than 34 is equal to the probability of obtaining a z-score greater than z = 2.00 from a normal distribution.

The law of large numbers states that the larger the sample size (n),the more probable it is that the sample mean will be close to the population mean..

A random sample of n = 4 scores is selected from a population.Which of the following distributions will definitively be normal?​

A mathematical proposition known as the central limit theorem provides a precise description of the distribution that would be obtained if you selected every possible sample,calculated every sample mean,and constructed the distribution of the sample mean.

If the standard deviation for a population increases,the standard error for sample means from the population will also increase.

A sample of n = 4 scores is selected from a population with µ = 70 and s = 10.The probability of obtaining a sample mean greater than 65 is p = 0.8413.

What happens to the expected value of M as sample size increases?​

A random sample of n = 4 scores is obtained from a normal population with µ = 20 and σ = 4.What is the probability that the sample mean will be greater than M = 22?​

The smallest possible standard error is obtained when a small sample is taken from a population with a small standard deviation.

A researcher obtained M = 27 for a sample of n = 36 scores selected from a population with µ = 30 and s = 18.This sample mean corresponds to a z-score of z = -1.00.

For a population with µ = 80 and σ = 20,the distribution of sample means based on n = 16 will have an expected value of ____ and a standard error of ____.​

A sample of n = 9 scores is obtained from a population with μ = 70 and σ = 18.If the sample mean is M = 76,then what is the z-score for the sample mean?​

If random samples,each with n = 36 scores,are selected from a normal population with µ = 80 and σ = 18,how much difference,on average,should there be between a sample mean and the population mean?​

A sample of n = 4 scores is selected from a population with μ = 50 and σ = 12.If the sample mean is M = 56,what is the z-score for this sample mean?​

The distribution of sample means is the collection of sample means for all the possible random samples of a particular size (n)that can be obtained from a population.

The mean for a sample of n = 4 scores has a standard error σM = 5 points.This sample was selected from a population with a standard deviation of σ = 20.

A sample is obtained from a population with s = 20.If the sample mean has a standard error of 5 points,then the sample size is n = 4.

The distribution of sample means ____.​

A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 6.What is the probability that the sample mean will be greater than M = 43?​

Introduction to Statistics

Frequency Distributions

Central Tendency

Variability

Z-Scores: Location of Scores and Standardized Distributions

Probability

Introduction to Hypothesis Testing

Introduction to the T Statistic

The T Test for Two Independent Samples

The T Test for Two Related Samples

Introduction to Analysis of Variance

Repeated-Measures Analysis of Variance Anova

Two-Factor Analysis of Variance Independent Measures

Correlation

Introduction to Regression

The Chi-Square Statistic: Tests for Goodness of Fit and Independence

The Binomial Test

Filters

A random sample of n = 4 scores is selected from a population.Which of the following distributions will definitively be normal?

What happens to the expected value of M as sample size increases?

A random sample of n = 4 scores is obtained from a normal population with µ = 20 and σ = 4.What is the probability that the sample mean will be greater than M = 22?

For a population with µ = 80 and σ = 20,the distribution of sample means based on n = 16 will have an expected value of and a standard error of .

A sample of n = 9 scores is obtained from a population with μ = 70 and σ = 18.If the sample mean is M = 76,then what is the z-score for the sample mean?

If random samples,each with n = 36 scores,are selected from a normal population with µ = 80 and σ = 18,how much difference,on average,should there be between a sample mean and the population mean?

A sample of n = 4 scores is selected from a population with μ = 50 and σ = 12.If the sample mean is M = 56,what is the z-score for this sample mean?

The mean for a sample of n = 4 scores has a standard error σ_M = 5 points.This sample was selected from a population with a standard deviation of σ = 20.

The distribution of sample means ____.

A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 6.What is the probability that the sample mean will be greater than M = 43?