Exam 8: Confidence Interval Estimation

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Confidence intervals are a function of the

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If the standard error of the sampling distribution of the sample proportion If the standard error of the sampling distribution of the sample proportion   is 0.0324 for samples of size 200,then the population proportion must be 0.30. is 0.0324 for samples of size 200,then the population proportion must be 0.30.

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A confidence interval is an interval that,with a stated level of confidence,captures a population parameter.

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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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The chi-square distribution for developing a confidence interval for a standard deviation has degrees of freedom equal to

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You would like to estimate the average amount a family spends on food during a year.In the past,the standard deviation of the amount a family has spent on food during a year has been approximately $800.If you want to be 95% sure that you estimated average family food expenditures within $50,how many families do you need to survey?

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Generally speaking,the two types of statistical inference are

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In general,increasing the confidence level will narrow the confidence interval,and decreasing the confidence level widens the interval.

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In developing a confidence interval for the population standard deviation In developing a confidence interval for the population standard deviation   ,we make use of the fact that the sampling distribution of the sample standard deviation s is not the normal distribution or the t-distribution,but rather a right-skewed distribution called the chi-square distribution,which (for this procedure)has n - 1 degrees of freedom. ,we make use of the fact that the sampling distribution of the sample standard deviation s is not the normal distribution or the t-distribution,but rather a right-skewed distribution called the chi-square distribution,which (for this procedure)has n - 1 degrees of freedom.

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If two random samples of size 40 each are selected independently from two populations whose variances are 35 and 45,then the standard error of the sampling distribution of the sample mean difference, If two random samples of size 40 each are selected independently from two populations whose variances are 35 and 45,then the standard error of the sampling distribution of the sample mean difference,   ,equals 1.4142. ,equals 1.4142.

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When you calculate the sample size for a proportion,you use an estimate for the population proportion; namely When you calculate the sample size for a proportion,you use an estimate for the population proportion; namely   .A conservative value for n can be obtained by using  .A conservative value for n can be obtained by using When you calculate the sample size for a proportion,you use an estimate for the population proportion; namely   .A conservative value for n can be obtained by using

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Suppose there are 500 accounts in a population.You sample 50 of them and find a sample mean of $500.What would be your estimate for the population total?

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The interval estimate 18.5 The interval estimate 18.5   2.5 is developed for a population mean in which the sample standard deviation s is 7.5.Had s equaled 15 instead,the interval estimate would be 37   5.0. 2.5 is developed for a population mean in which the sample standard deviation s is 7.5.Had s equaled 15 instead,the interval estimate would be 37 The interval estimate 18.5   2.5 is developed for a population mean in which the sample standard deviation s is 7.5.Had s equaled 15 instead,the interval estimate would be 37   5.0. 5.0.

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If two samples contain the same number of observations,then the data must be paired.

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You are attempting to estimate the average amount a family spends on food during a year.In the past,the standard deviation of the amount a family has spent on food during a year has been approximately $1200.If you want to be 99% sure that you have estimated average family food expenditures within $60,how many families do you need to survey?

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If a random sample of size 250 is taken from a population,where it is known that the population proportion p = 0.4,then the mean of the sampling distribution of the sample proportion If a random sample of size 250 is taken from a population,where it is known that the population proportion p = 0.4,then the mean of the sampling distribution of the sample proportion   is 0.60. is 0.60.

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If you are constructing a confidence interval for a single mean,the length of the confidence interval will _____ with an increase in the sample size.

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As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion   only if the sample size n is greater than 30. only if the sample size n is greater than 30.

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If two random samples of sizes 30 and 35 are selected independently from two populations whose means are 85 and 90,then the mean of the sampling distribution of the sample mean difference, If two random samples of sizes 30 and 35 are selected independently from two populations whose means are 85 and 90,then the mean of the sampling distribution of the sample mean difference,   ,equals 5. ,equals 5.

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If we cannot make the strong assumption that the variances of two samples are equal,then we must use the pooled standard deviation in calculating the standard error of a difference between the means.

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