Exam 8: Confidence Interval Estimation

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The 95% confidence interval for the population mean μ\mu ,given that the sample size n = 49 and the population standard deviation σ=7, is Xˉ±1.96\sigma = 7 \text {, is } \bar { X } \pm 1.96

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Two independent samples of sizes 50 and 50 are randomly selected from two populations to test the difference between the population means, μ1μ2\mu _ { 1 } - \mu _ { 2 } )The sampling distribution of the sample mean difference xˉ1xˉ2\bar { x } _ { 1 } - \bar { x } _ { 2 } Is:

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If you increase the confidence level,the confidence interval:

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If the standard error of the sampling distribution of the sample proportion pp^\hat { pp } is 0.0324 for samples of size 200,then the population proportion must be 0.30.

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In general,the paired-sample procedure is appropriate when the samples are naturally paired in some way and there is a reasonably large positive correlation between the pairs.In this case,the paired-sample procedure makes more efficient use of the data and generally results in narrower confidence intervals.

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In developing confidence interval for the difference between two population means using two independent samples,we use the pooled estimate sps _ { p } in estimating the standard error of the sampling distribution of the sample mean difference xˉ1xˉ2\bar { x } _ { 1 } - \bar { x } _ { 2 } if the populations are normal with equal variances.

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If you decrease the confidence level,the confidence interval .

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The degrees of freedom for the t and chi-square distributions is a numerical parameter of the distribution that defines the precise shape of the distribution.

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Two independent samples of sizes 20 and 25 are randomly selected from two normal populations with equal variances.In order to test the difference between the population means,the test statistic is:

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When samples of size n are drawn from a population,then the sampling distribution of the sample mean xx is approximately normal,provided that n is reasonably large.

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When we replace σ\sigma With the sample standard deviation (s),we introduce a new source of variability and the sampling distribution becomes the:

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Confidence intervals are a function of which of the following three things?

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The general form of a confidence interval is:

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