Exam 8: Estimating Single Population Parameters

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.

If the population is not normally distributed,the t-distribution cannot be used.

When determining the sample size for a proportion,if you have no previous information available to estimate p,then the best value to use is π = 0.5.

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. Suppose the airline also noted whether the passenger was male or female.Out of the 1,000 passengers observed,690 were males.Of this group,280 had more than one bag.Using this data,obtain and interpret a 95% confidence interval estimate for the proportion of male passengers in the population who would have been affected by the one-bag limit.

When determining sample size for a proportion,the farther that p is from 0.5,the smaller the resulting sample size will be.

In a recent audit report,an accounting firm stated that the mean sale per customer for the client was estimated to be between $14.50 and $28.50.Further,this was based on a random sample of 100 customers and was computed using 95 percent confidence.Provide a correct interpretation of this confidence interval estimate.

When calculating a confidence interval,the reason for using the t-distribution rather than the normal distribution for the critical value is that the population standard deviation is unknown.

A report in a consumer magazine indicated that with 90 percent confidence,the mean number of hours that a particular brand light bulb lasts is between 900 and 1,100 hours.Based on this,the sample mean that produced this estimate is 1,000 hours.

A study was recently conducted to estimate the mean cholesterol for adult males over the age of 55 years.From a random sample of n = 10 men,the sample mean was found to be 242.6 and the sample standard deviation was 73.33.To find the 95 percent confidence interval estimate for the mean,the correct critical value to use is:

When finding sample size,cutting the margin of error in half requires that the sample size be four times larger.

A regional hardware chain is interested in estimating the proportion of their customers who own their own homes.There is some evidence to suggest that the proportion might be around 0.70.Given this,what sample size is required if they wish a 90 percent confidence level with a margin of error of ±.025?

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 Parks and Recreation official surveyed 200 people at random who have used one of the city's parks.The survey revealed that 26 resided outside the city limits.If she had to arrive at one single value to estimate the true proportion of park users who are residents of the city it would be 0.13.

In an application to estimate the mean number of miles that downtown employees commute to work roundtrip each day,the following information is given: n = 20 = 4.33 S = 3.50 Based on this information,the upper limit for a 95 percent confidence interval estimate for the true population mean is:

Allante Pizza delivers pizzas throughout its local market area at no charge to the customer.However,customers often tip the driver.The owner is interested in estimating the mean tip income per delivery.To do this,she has selected a simple random sample of 12 deliveries and has recorded the tips that were received by the drivers.These data are: Based on these sample data,what is the best point estimate to use as an estimate of the true mean tip per delivery?

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?

A random sample of 100 people was selected from a population of customers at a local bank.The mean age of these customers was 40.If the population standard deviation is thought to be 5 years,the margin of error for a 95 percent confidence interval estimate is .98 year.

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?

A survey of 499 women for the American Orthopedic Foot and Ankle Society revealed that 38% wear flats to work. Use this sample information to develop a 99% confidence interval for the population proportion of women who wear flats to work.

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 margin of error for the estimate is approximately ±.1061.