Exam 8: Estimating Single Population Parameters

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

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

In determining the required sample size in an application involving an estimate for the population mean,if the population standard deviation is known,there is no compelling reason to select a pilot sample.

The manager in charge of concessions at an NFL football stadium is interested in estimating the mean dollars that are spent per person attending the games.A pilot sample of n = 50 people has revealed a sample mean and standard deviation of $12.35 and $2.35 respectively.He wishes to estimate the population mean within ± $0.20 of the true mean and wishes to have a confidence level of 95 percent.Given this,he needs to sample an additional 481 people.

All of the factors that are needed to determine the required sample size are within the control of the decision maker.

When estimating sample size,a 90 percent confidence level will result in a smaller sample size than a 95 percent confidence level.

When σ is unknown,one should use an estimate that is considered to be at least as large as the true σ.This will provide a conservative sample size to be on the safe side.

The file Danish Coffee contains a random sample of 144 Danish coffee drinkers and measures the annual coffee consumption in kilograms for each sampled coffee drinker.A marketing research firm wants to use this information to develop an advertising campaign to increase Danish coffee consumption. Develop and interpret a 90% confidence interval estimate for the mean annual coffee consumption of Danish coffee drinkers.

Chicago Connection,a local pizza company,delivers pizzas for free within the market area.The delivery drivers are paid $2.00 per delivery plus they get to keep any tips.To estimate the proportion of deliveries that result in a tip to the driver,a random sample of 64 deliveries was selected.Of these,48 times a tip was received.Based on this information,and using a 95 percent confidence level,the upper limit for the confidence interval estimate is about .1061.

A production process that fills 12-ounce cereal boxes is known to have a population standard deviation of 0.009 ounce.If a consumer protection agency would like to estimate the mean fill,in ounces,for 12-ounce cereal boxes with a confidence level of 92% and a margin of error of 0.001,what size sample must be used?

In developing a confidence interval estimate,the margin of error is directly dependent on the value of the point estimate.

A hospital emergency room has collected a sample of n = 40 to estimate the mean number of visits per day.It has found the standard deviation is 32.Using a 90 percent confidence level,what is its margin of 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 determining the required sample size when estimating a population proportion,it is necessary to start with some idea of what that proportion is.

A random sample of n = 500 people was surveyed recently to determine an estimate for the proportion of people in the population who had attended at least some college.The estimate concluded that between 0.357 and 0.443 of the population had attended.Given this information,we can determine that the confidence level was approximately 95 percent.

Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size)onto the plane.However,their studies show that the more carry-on baggage passengers have,the longer it takes to unload and load passengers.One regional airline is considering changing its policy to allow only one carry-on per passenger.Before doing so,it decided to collect some data.Specifically,a random sample of 1,000 passengers was selected.The passengers were observed,and the number of bags carried on the plane was noted.Out of the 1,000 passengers,345 had more than one bag. The domestic version of Boeing's 747 has a capacity for 568 passengers.Determine an interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane.Assume the plane is at its passenger capacity.

The Wisconsin Dairy Association is interested in estimating the mean weekly consumption of milk for adults over the age of 18 in that state.To do this,they have selected a random sample of 300 people from the designated population.The following results were recorded: Given this information,if the leaders wish to estimate the mean milk consumption with 90 percent confidence,what is the approximate margin of error in the estimate?

A random sample of 100 boxes of cereal had a sample mean weight of 396 grams.The standard deviation is known to be 5 grams.The upper end of the confidence interval for the mean is 405.8 grams.

After taking a speed-reading course,students are supposed to be able to read faster than they could before taking the course.A pilot sample of n = 25 students showed a mean increase of 300 words per minute with a standard deviation equal to 60 words per minute.To estimate the population mean with 95 percent confidence and a margin of error of ±10 minutes,the required sample size is approximately 139 students.

A publisher is interested in estimating the proportion of textbooks that students resell at the end of the semester.He is interested in making this estimate using a confidence level of 95 percent and a margin of error of ±0.02.Based upon his prior experience,he believes that π is somewhere around 0.60.Given this information,the required sample size is over 2,300 students.