Exam 8: Sampling Distributions

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The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .3 inches. What is the probability that the average length of a steel sheet from a sample of 9 steel sheets is more than 29.95 inches long?

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The spread of the sampling distribution of The spread of the sampling distribution of   is ________ the spread of the corresponding population distribution sampling distribution. is ________ the spread of the corresponding population distribution sampling distribution.

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A sample size of 500 is sufficiently large to conclude that the sampling distribution of A sample size of 500 is sufficiently large to conclude that the sampling distribution of   is a normal distribution, when the estimate of the population proportion is .995. is a normal distribution, when the estimate of the population proportion is .995.

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As the sample size ________, the variation of the sampling distribution of As the sample size ________, the variation of the sampling distribution of   ________. ________.

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The ________ is the probability distribution of the population of all possible sample means that could be obtained from all possible samples of the same size.

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If we have a sample size of 100 and the estimate of the population proportion is .10, what is the mean of the sampling distribution of the sample proportion?

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The population of all sample proportions has a normal distribution if the sample size (n) is sufficiently large. The rule of thumb for ensuring that n is sufficiently large is

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The ________ is a minimum-variance unbiased point estimate of the mean of a normally distributed population.

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A random sample of size 1,000 is taken from a population where p = .20. Find P( A random sample of size 1,000 is taken from a population where p = .20. Find P(   < .22). < .22).

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A random sample of size 1,000 is taken from a population where p = .20. What is A random sample of size 1,000 is taken from a population where p = .20. What is   ? ?

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The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .2 inches. A sample of 4 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.25 and 30.35 inches long?

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A random sample of size 1,000 is taken from a population where p = .20. Find P( A random sample of size 1,000 is taken from a population where p = .20. Find P(   > .21). > .21).

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If the sample size n is infinitely large, then s2 is an unbiased estimator of σ2.

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A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P(   < 48). < 48).

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A sample statistic is an unbiased point estimate of a population parameter if the mean of the populations of all possible values of the sample statistic equals the population parameter.

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The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are more than 90 days overdue (delinquent). The historical records of the company show that over the past 8 years, the average has been that 14 percent of the accounts have been delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What are the mean and the standard deviation of the sampling distribution of The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are more than 90 days overdue (delinquent). The historical records of the company show that over the past 8 years, the average has been that 14 percent of the accounts have been delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What are the mean and the standard deviation of the sampling distribution of   ? ?

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A random sample of size 36 is taken from a population with a mean of 50 and a standard deviation of 5. The sampling distribution of A random sample of size 36 is taken from a population with a mean of 50 and a standard deviation of 5. The sampling distribution of   ________. ________.

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Find P( Find P(   < 35) if μ = 40, σ<sub>x</sub> = 16, n = 16. < 35) if μ = 40, σx = 16, n = 16.

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A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P(   > 50.5). > 50.5).

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The reason sample variance has a divisor of n − 1 rather than n is that it makes the variance an unbiased estimate of the population variance.

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