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Exam 8: Large-Sample Estimation

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Question 51

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A 90% confidence interval for the population mean is found to be between 5.28 and 6.72. Based on this information, the sample mean that generated the confidence interval was 6.

A) True
B) False

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Question 52

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For a given sample size and given confidence coefficient, the closer the population proportion p to 1.0, the greater the margin of error will be.

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B) False

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Question 53

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A study was conducted to compare the mean numbers of police emergency calls per 8-hour shift in two districts of Los Angeles. Samples of 100 8-shifts were randomly selected from the police records for each of the two regions, and the number of emergency calls was recorded for each shift. The sample statistics are listed below: Find a 90% confidence interval for the difference in the mean numbers of police emergency calls per shift between the two districts of the city. ______________ Interpret the interval. ________________________________________________________

In developing an interval estimate for a population mean, the population standard deviation was 8. The interval estimate was 40.52 3.24. Had equaled 16, the interval estimate would be:

A 90% upper confidence bound (UCB) for the population proportion p can be constructed using the following equation: UCB =

A random sample of n = 50 observations from a quantitative population produced = 65.4 and s² = 2.8. Give the best point estimate for the population mean, . ______________ Calculate the margin of error. ______________

The two limits that define an interval estimate are known as confidence limits.

A 90% confidence interval estimate for a population mean is determined to be 62.8 to 73.4. If the confidence level is reduced to 80%, the confidence interval for becomes narrower.

A statistic is said to be unbiased if its sampling distribution has the smallest standard error.

Which of the following is a parameter?

A stylist at The Hair Care Palace gathered data on the number of hair colorings given on Saturdays and on weekdays. Her results are listed below. Assume the two samples were independently taken from normal populations. Find the point estimate of p₁ - p₂. ______________ Find the margin of error. ______________ Estimate the difference in the true proportions with a 99% confidence interval. ______________ Interpret this interval. ________________________________________________________

Suppose a 95% confidence interval for the mean height of a 12-year-old male in the United States is 54 to 65 inches. In repeated sampling, 95% of the intervals constructed will contain the interval from 54 to 65 inches.

The wider the confidence interval, the more likely it is that the interval contains the true value of the population parameter.

Those who engage in estimation insist on random sampling, rather than convenience sampling or judgment sampling, because random sampling:

The concept of margin of error applies directly when estimating the population mean , but is not applicable when estimating the population proportion p.

The manufacturer of a particular battery pack for a laptop computer claims the battery pack can function for 8 hours, on the average, before having to be recharged. A random sample of 36 such battery packs was selected and tested. The mean and standard deviation were found to be 6 hours and 1.8 hours, respectively. Find a 95% lower confidence bound for the true average time the battery pack can function before having to be recharged. ______________

A recent survey indicates that the proportion of season ticket holders for Ferris State University hockey team that renew their seats is about .80. Using this information, the sample size that is needed to estimate the true proportion that plan to renew their seats using 95% confidence and a margin of error of .025 is about:

A proportion of a college basketball team's season ticket holders renew their tickets for the next season. Let p denote the true proportion of ticket holders who buy tickets again for the following season. A random sample of 125 ticket holders revealed 90 people plan on renewing their tickets. Give a point estimate for p and find the estimated margin of error. The point estimate is: ______________ The margin of error is: ______________

Suppose that a 95% confidence interval for the population proportion p is given by . This notation means that we are 95% confident that p falls between and .

The margin of error is: