Exam 8: Estimating Single Population Parameters

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.

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.

The Hilbert Drug Store owner plans to survey a random sample of his customers with the objective of estimating the mean dollars spent on pharmaceutical products during the past three months. He has assumed that the population standard deviation is known to be $15.50. Given this information, what would be the required sample size to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00?

In estimating a population mean, a large sample size is generally preferable to a small sample size because the margin of error is generally smaller.

Assuming the population of interest is approximately normally distributed, construct a 95% confidence interval estimate for the population mean given the following values:

Twenty one (21) customers out of a simple random sample of 50 said that they came to the grocery store within one month after getting a card from the company. Based on the data, the marketing manager thinks that the number of total customers who would come in to the grocery store within one month is 4,200 because 10,000 cards were mailed.

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.

The purpose of a pilot sample is:

A traffic engineer plans to estimate the average number of cars that pass through an intersection each day. Based on previous studies the standard deviation is believed to be 52 cars. She wants to estimate the mean to within ±10 cars with 90 percent confidence. The needed sample size for n is:

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.

Which of the following will result in a larger margin of error in an application involving the estimation of a population mean?

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.

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.

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?

If a population is skewed, the point estimate will be pushed to the right or left of the middle of the confidence interval estimate.

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

The manager of a toy store wants to estimate the population mean of daily online customers by using a 90% confidence interval estimate that has a margin of error of ±50.0. If the population standard deviation is thought to be 300, what is the required sample size?

The higher the level of confidence, the wider the confidence interval must be.

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.

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