Exam 7: Sampling Distribution of Means

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A standardized assessment inventory on the personality characteristic of "Perfectionism" has a μ = 70 and a σ = 12. a. Compute σM for a sample of n = 100. b. Compute σM for a sample of n = 25. c. How is σM affected by sample size?

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a. σM=12100=1.2\sigma_{M}=\frac{12}{\sqrt{100}}=1.2 b. σM=1225=2.4\sigma_{M}=\frac{12}{\sqrt{25}}=2.4 c. As the size of the sample increases, the amount of standard error decreases.

The symbol that represents the standard error of the mean is _______.

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A

A normally shaped distribution has a μ = 36 and a σ = 12. A sample of 9 individuals is randomly selected and achieved a M = 32. What is the z-score for the obtained sample mean?

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C

Standard error

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The standard deviation for a set of scores is 10 and the sample size is 42. What is the standard error of the mean?

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The symbol that represents the expected value of a sampling distribution of means is _____.

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Given the same standard deviation for two different distributions, as the size of the sample decreases

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The standard error of the mean is based on the

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The standard deviation of the sampling distribution of means is called the ______________.

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A random sample of size n = 40 is randomly drawn from a population that is normally distributed with a μ = 82 and a σ = 13. The probability is .02 that the sample mean will be above what value?

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The central limit theorem covers all of the following aspects of the sampling distribution of means, except the

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A random sample of size n = 48 is drawn from a normally shaped distribution with a μ = 110 and a σ = 17. What is the probability that the mean of the sample will be greater than 104?

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A population distribution is normally distributed with a μ = 93 and a σ = 13. If n = 50, what proportion of sample means can be expected to be less than 97?

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A sample of n = 25 is selected at random from a population with a σ = 15. Approximately how much difference in the scores would you expect between the sample mean and the population mean?

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A sample of n = 9 is drawn at random from a population with a μ = 32 and a σ = 9. The probability that the sample mean will be 34 or below is _________.

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Given a population mean of 78 and a standard error of the mean value of 2, what else do we need to use the formula to find the range of means that would be expected to occur 90% of the time?

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If we added up all of our means from a sampling distribution of means and divided by the number that represented all possible samples, the result would be the _______________.

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M = μ + (z)(σM) is used to

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The sampling distribution of means is

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In order to use the z-score formula for determining the probability of obtaining a sample mean, we need all of the following, except _____________.

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