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Exam 8: Estimating Single Population Parameters

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Question 71

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In estimating a population proportion,the factors that are needed to determine the required sample size are the confidence level,the margin of error and some idea of what the population proportion is.

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Question 72

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The t-distribution is used to obtain the critical value in developing a confidence interval when the population distribution is not known or the sample size is small.

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Question 73

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The margin of error is one-half the width of the confidence interval.

An advertising company wishes to estimate the mean household income for all single working professionals who own a foreign automobile.If the advertising company wants a 90% confidence interval estimate with a margin of error of ±$2,500,what sample size is needed if the population standard deviation is known to be $27,500?

A cell phone service provider has selected a random sample of 20 of its customers in an effort to estimate the mean number of minutes used per day.The results of the sample included a sample mean of 34.5 minutes and a sample standard deviation equal to 11.5 minutes.Based on this information,and using a 95 percent confidence level:

A 95 percent confidence interval for a mean will contain 95 percent of the population within the interval.

Recently,a marketing research company reported that based on a random sample of 300 households the mean number of trips to a major shopping mall per month per household is 4.12 trips.This value is referred to as a parameter and is subject to sampling error.

In an effort to estimate the mean dollars spent per visit by customers of a food store,the manager has selected a random sample of 100 cash register receipts.The mean of these was $45.67 with a sample standard deviation equal to $12.30.Assuming that he wants to develop a 90 percent confidence interval estimate,which of the following is the margin of error that will be reported?

When developing a confidence interval estimate,the confidence level is calculated based on the size of the sample and the population standard deviation.

According to USA Today,customers are not settling for automobiles straight off the production lines.As an example,those who purchase a $355,000 Rolls-Royce typically add $25,000 in accessories.One of the affordable automobiles to receive additions is BMW's Mini Cooper.A sample of 179 recent Mini purchasers yielded a sample mean of $5,000 above the $20,200 base sticker price.Suppose the cost of accessories purchased for all Mini Coopers has a standard deviation of $1,500. Calculate a 95% confidence interval for the average cost of accessories on Mini Coopers.

What sample size is needed to estimate a population mean within ±50 of the true mean value using a confidence level of 95%,if the true population variance is known to be 122,500?

A human resources manager wishes to estimate the proportion of employees in her large company who have supplemental health insurance.What is the largest size sample she should select if she wants 95 percent confidence and a margin of error of ± 0.01?

A financial analyst is interested in estimating the proportion of publicly traded companies on the New York Stock Exchange that have cash balances that are more than 10 percent of the total assets of the company.A random sample of n = 100 companies shows that 13 had cash balances of more than 10 percent of assets.Based on this information,develop and interpret a 90 percent confidence interval estimate for the population proportion.

The one sure thing that can be said about a point estimate is that it will most likely be subject to sampling error and not equal the parameter.

When small samples are used to estimate a population mean,in cases where the population standard deviation is unknown:

When determining sample size for a proportion,using p = 0.5 will produce the smallest possible value for n.

The concept of margin of error applies directly when estimating a population mean,but is not appropriate when estimating a population proportion.

A study was recently conducted to estimate the mean cholesterol for adult males over the age of 55 years.The following random sample data were observed: Given this information,what is the point estimate for the population mean?

In an effort to estimate the mean dollars spent per visit by customers of a food store,the manager has selected a random sample of 100 cash register receipts.The mean of these was $45.67 with a sample standard deviation equal to $12.30.Assuming that he wants to develop a 90 percent confidence interval estimate,the upper limit of the confidence interval estimate is:

A major tire manufacturer wishes to estimate the mean tread life in miles for one of its tires.It wishes to develop a confidence interval estimate that would have a maximum sampling error of 500 miles with 90 percent confidence.A pilot sample of n = 50 tires showed a sample standard deviation equal to 4,000 miles.Based on this information,the required sample size is: