Exam 9: Introduction to Estimation

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Physicians: A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year. -Can we conclude at the 1% significance level that the true proportion of physicians in the population who make at least $400,000 a year is less than 0.24?

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The formula The formula   is used to find the ____________________ to estimate a population proportion. is used to find the ____________________ to estimate a population proportion.

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If the population standard deviation is guesstimated, and it turned out to be smaller than you assumed, then the sample size you calculated is ____________________ than it needs to be.

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A point estimator is defined as:

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When a population is small, it is necessary to include the ____________________ factor in our hypothesis tests and confidence interval estimators for p.

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An unbiased estimator of a population parameter is defined as:

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The sample mean  The sample mean   is a consistent estimator of the population mean  \mu . is a consistent estimator of the population mean μ\mu .

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An estimator is said to be consistent if:

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Is the sample mean a consistent estimator of the population mean? Explain

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If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.

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Draw the sampling distribution of two unbiased estimators for μ\mu , one of which is relatively efficient.

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An interval estimator estimates the value of an unknown ____________________.

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The test statistic for p is approximately normal when ____________________ and ____________________ are both greater than 5.

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The sample proportion The sample proportion   is a consistent estimator of the population proportion p because it is unbiased and the variance of   is p(1 - p) / n, which grows smaller as n grows larger. is a consistent estimator of the population proportion p because it is unbiased and the variance of The sample proportion   is a consistent estimator of the population proportion p because it is unbiased and the variance of   is p(1 - p) / n, which grows smaller as n grows larger. is p(1 - p) / n, which grows smaller as n grows larger.

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The sample variance (where you divide by n - 1) is an unbiased estimator of the population variance.

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Statisticians can control the ____________________ of a confidence interval by determining the sample size necessary to produce the desired results.

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An interval estimate is an estimate of the range for a sample statistic.

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Draw a sampling distribution of a biased estimator for μ\mu .

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The sampling error for a confidence interval is also defined as the ____________________ of ____________________.

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Estimating or testing for p is used in situations when the data are ____________________.

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