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

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Question 31

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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.

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B) False

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Question 32

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

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B) False

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Question 33

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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.

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.

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 ____.​

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)?

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.

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 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..

The distribution of sample means ____.​

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

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 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?​

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?​

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.

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

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.

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?​

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?​

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