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Exam 8: Estimating Single Population Parameters

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Question 21

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One of the major oil products companies conducted a study recently to estimate the mean gallons of gasoline purchased by customers per visit to a gasoline station.To do this,a random sample of customers was selected with the following data being recorded that show the gallons of gasoline purchased. Based on these sample data,construct and interpret a 95 percent confidence interval estimate for the population mean.

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Since the population standard deviation ...

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Question 22

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Recently,a report in a financial journal indicated that the 90 percent confidence interval estimate for the proportion of investors who own one or mutual funds is between 0.88 and 0.92.Given this information,the sample size that was used in this study was approximately 609 investors.

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Question 23

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The fact that a point estimate will likely be different than the corresponding population value is due to the fact that point estimates are subject to sampling error.

Confidence intervals constructed with small samples tend to have greater margins of error than those constructed from larger samples,all else being constant.

In an effort to estimate the mean length of stay for motel guests at a major national motel chain,the decision makers asked for a 95 percent confidence,and a margin of error of ± 0.25 days.Further,it was known that the population standard deviation is 0.50 days.Given this,the required sample size to estimate the mean length of stay is about 16 customers.

In developing a confidence interval estimate for the population mean,the t-distribution is used to obtain the critical value when:

A university computer lab manager wishes to estimate the mean time that students stay in the lab per visit.She believes that the population standard deviation would be no larger than 10 minutes.Further,she wishes to have a confidence level of 90 percent and a margin of error of ± 2.00 minutes.Given this,the sample size that she uses is approximately 60 students.

An educational organization in California is interested in estimating the mean number of minutes per day that children between the age of 6 and 18 spend watching television per day.A previous study showed that the population standard deviation was 21.5 minutes.The organization selected a random sample of n = 200 children between the age of 6 and 18 and recorded the number of minutes of TV that each person watched on a particular day.The mean time was 191.3 minutes.If the leaders of the organization wish to develop an interval estimate with 95 percent confidence,what will the margin of error be?

A point estimate for the population mean will always fall within the confidence interval estimate.

A sample of 250 people resulted in a confidence interval estimate for the proportion of people who believe that the federal government's proposed tax increase is justified is between 0.14 and 0.20.Based on this information,what was the confidence level used in this estimation?

The following data represent a random sample of bank balances for a population of checking account customers at a large eastern bank.Based on these data,what is the critical value for a 95 percent confidence interval estimate for the true population mean?

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

In determining the sample size requirement for an application involving the estimation of the proportion of department store customers who pay using the store's credit card,the closer the true proportion is to .5,the larger will be the required sample size for a given margin of error and confidence level.

In a sample size determination situation,reducing the margin of error by half will double the required sample size.

Which of the following statements is true with respect to the confidence level associated with an estimation application?

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

A point estimate is equally likely to be higher or lower than the population mean if the sampling is done using a statistical sampling procedure.

A popular restaurant takes a random sample n = 25 customers and records how long each occupied a table.The found a sample mean of 1.2 hours and a sample standard deviation of 0.3 hours.Find the 95 percent confidence interval for the mean.

The produce manager for a large retail food chain is interested in estimating the percentage of potatoes that arrive on a shipment with bruises.A random sample of 150 potatoes showed 14 with bruises.Based on this information,what is the margin of error for a 95 percent confidence interval estimate?

Sampling error occurs when: