Exam 8: Estimating Single Population Parameters

In estimating a population mean,increasing the confidence level will result in a higher margin of error for a given sample size.

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

A large Midwestern university is interested in estimating the mean time that students spend at the student recreation center per week.A previous study indicated that the standard deviation in time is about 40 minutes per week.If the officials wish to estimate the mean time within ± 10 minutes with a 90 percent confidence,what should the sample size be?

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. Determine the margin of error in estimating the average cost of accessories on Mini Coopers.

Construct a 98% confidence interval estimate for the population mean given the following values:

A local pizza company is interested in estimating the percentage of customers who would take advantage of a coupon offer.To do this,they give the coupon out to a random sample of 100 customers.Of these,45 actually use the coupon.Based on a 95 percent confidence level,the upper and lower confidence interval limits are approximately 0.3525 to 0.5475.

A random sample of 340 people in Chicago showed that 66 listened to WJKT-1450,a radio station in South Chicago Heights.Based on this sample information,what is the point estimate for the proportion of people in Chicago that listen to WJKT-1450?

As the automobile accident rate increases,insurers are forced to increase their premium rates.Companies such as Allstate have recently been running a campaign they hope will result in fewer accidents by their policyholders.For each six-month period that a customer goes without an accident,Allstate will reduce the customer's premium rate by a certain percentage.Companies like Allstate have reason to be concerned about driving habits,based on a survey conducted by Drive for Life,a safety group sponsored by Volvo of North America,in which 1,100 drivers were surveyed.Among those surveyed,74% said that careless or aggressive driving was the biggest threat on the road.One-third of the respondents said that cell phone usage by other drivers was the driving behavior that annoyed them the most. Based on these data,assuming that the sample was a simple random sample,construct and interpret a 95% confidence interval estimate for the true proportion in the population of all drivers who are annoyed by cell phone users.

In a recent report to the supply-chain manager in a major electronics company,the report writer stated that with 90 percent confidence,the manufacturing lead time for a critical part is between 3.34 hours and 4.14 hours.Based on this information,the margin of error for this estimate is ±.80 hours.

What are the disadvantages of using a small sample to estimate the population mean?

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

A decision maker is interested in estimating a population proportion.A sample of size n = 150 yields 115 successes.Based on these sample data,construct a 90% confidence interval estimate for the true population proportion.

A bank manager wishes to estimate the mean waiting time spent by customers at his bank.He knows from previous experience that the standard deviation is about 4.0 minutes.If he desires a 90 percent confidence interval estimate and wishes to have a margin of error of 1 minute,the required sample size will be approximately 143.

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. Based on the sample's results,what is the best point estimate of average annual coffee consumption for Danish coffee drinkers?

In a situation where the population standard deviation is known and we wish to estimate the population mean with 90 percent confidence,what is the appropriate critical value to use?

The chamber of commerce in a beach resort town wants to estimate the proportion of visitors who are repeat visitors.From previous experience they believe the portion is in the vicinity of 0.5 and they want to estimate the proportion to within ± 0.03 percentage points with 95 percent confidence.The sample size they should use is:

To construct a 99 percent confidence interval where σ is known,the correct critical value is 1.96.

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 98 percent confidence,what would be the upper and lower limits of the interval estimate?

The makers of weight loss product are interested in estimating the mean weight loss for users of their product.To do this,they have selected a random sample of n = 9 people and have provided them with a supply of the product.After six months,the nine people had an average weight loss of 15.3 pounds with a standard deviation equal to 3.5 pounds.The upper limit for the 90 percent confidence interval estimate for the population mean is approximately 17.47 pounds.

If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean,she can: