Exam 8: Interval Estimation

From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population μ).

If the standard deviation of the lifetime of a vacuum cleaner is estimated to be 300 hours, how large of a sample must be taken in order to be 97% confident that the margin of error will not exceed 40 hours?

A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is

A local electronics firm wants to determine their average daily sales in dollars.) A sample of the sales for 36 days revealed average sales of $139,000. Assume that the standard deviation of the population is known to be $12,000. a. Provide a 95% confidence interval estimate for the average daily sales. b. Provide a 97% confidence interval estimate for the average daily sales.

Exhibit 8-6 A sample of 75 information system managers had an average hourly income of $40.75 with a standard deviation of $7.00. -Refer to Exhibit 8-6. The 95% confidence interval for the average hourly wage of all information system managers is

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 25 pieces of carry-on luggage was collected and weighed. The average weight was 18 pounds. Assume that we know the standard deviation of the population to be 7.5 pounds. a. Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage. b. Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.

The ability of an interval estimate to contain the value of the population parameter is described by the

A random sample of 81 credit sales in a department store showed an average sale of $68.00. From past data, it is known that the standard deviation of the population is $27.00. a. Determine the standard error of the mean. b. With a 0.95 probability, what can be said about the size of the margin of error? c. What is the 95% confidence interval of the population mean?

A random sample of 87 airline pilots had an average yearly income of $99,400 with a standard deviation of $12,000. a. If we want to determine a 95% confidence interval for the average yearly income, what is the value of t? b. Develop a 95% confidence interval for the average yearly income of all pilots.

The monthly starting salaries of students who receive an MBA degree have a population standard deviation of $110. What size sample should be selected to obtain a 0.95 probability of estimating the mean monthly income within $20 or less?

In a random sample of 100 observations, = 0.2. The 95.44% confidence interval for P is

It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is

A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favors Candidate A is

A university planner is interested in determining the percentage of spring semester students who will attend summer school. She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school. a. Construct a 95% confidence interval estimate for the percentage of spring semester students who will return to summer school. b. Using the results of the pilot study with a 0.95 probability, how large of a sample would have to be taken to provide a margin of error of 3% or less?

Many people who bought X-Game gaming systems over the holidays have complained that the systems they purchased were defective. In a sample of 1200 units sold, 18 units were defective. a. Determine a 95% confidence interval for the percentage of defective systems. b. If 1.5 million X-Games were sold over the holidays, determine an interval for the number of defectives in sales.

A simple random sample of 36 items resulted in a sample mean of 40 and a standard deviation of 12. Construct a 95% confidence interval for the population mean.

A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the standard deviation of the population is $40.00. a. Determine the standard error of the mean. b. With a 0.95 probability, determine the margin of error. c. What is the 95% confidence interval of the population mean?

An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the

Exhibit 8-4 In order to estimate the average electric usage per month, a sample of 81 houses was selected, and the electric usage was determined. Assume a population standard deviation of 450-kilowatt hours. -Refer to Exhibit 8-4. The standard error of the mean is

The z value for a 97.8% confidence interval estimation is