Exam 8: Interval Estimation

A random sample of 26 checking accounts at a bank showed an average daily balance of $300 and a standard deviation of $45. The balances of all checking accounts at the bank are normally distributed. Develop a 95% confidence interval estimate for the mean of the population.

Exhibit 8-1 In order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. -Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is approximately

A bank manager wishes to estimate the average waiting time for customers in line for tellers. A random sample of 50 times is measured and the average waiting time is 5.7 minutes. The population standard deviation of waiting time is 2 minutes. Which Excel function would be used to construct a confidence interval estimate?

You are given the following information obtained from a random sample of 4 observations from a large, normally distributed population. a.What is the point estimate of $\mu$ ? b.Construct a 95% confidence interval for $\mu$ . c.Construct a 90% confidence interval for $\mu$ . d.Discuss why the 90% and 95% confidence intervals are different.

It is known that the variance of a population equals 484. A random sample of 81 observations is going to be taken from the population. a.With a .80 probability, what statement can be made about the size of the margin of error? b.With a .80 probability, how large of a sample would have to be taken to provide a margin of error of 3 or less?

The margin of error in an interval estimate of the population mean is a function of all of the following except

The manager of University Credit Union (UCU) is concerned about checking account transaction discrepancies. Customers are bringing transaction errors to the attention of the bank's staff several months after they occur. The manager would like to know what proportion of his customers balance their checking accounts within 30 days of receiving a transaction statement from the bank.Using systematic random sampling, 400 checking account customers are contacted by telephone and asked if they routinely balance their accounts within 30 days of receiving a statement. 271 of the 400 customers respond Yes. a. Develop a 95% confidence interval estimate for the proportion of the population of checking account customers at UCU that routinely balance their accounts in a timely manner. b. Suppose UCU wants a 95% confidence interval estimate of the population proportion with a margin of error of E = .025. How large a sample size is needed?

Below you are given ages that were obtained by taking a random sample of 9 undergraduate students. Use Excel to determine an interval estimate for the mean of the population at a 99% confidence level. Interpret your results.

The confidence associated with an interval estimate is called the

Exhibit 8-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is one minute. -Refer to Exhibit 8-2. The 95% confidence interval for the average checkout time of all customers is

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

For which of the following values of p is the value of p(1 - p) maximized?

For inventory purposes, a grocery store manager wants to estimate the mean number of pounds of cat food sold per month. The estimate is desired to be within 10 pounds with a 95% level of confidence. A pilot study provided a standard deviation of 27.6 pounds. How many months should be sampled?

A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to 0.90, the interval for $\sigma$

Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. -Refer to Exhibit 8-3. If the sample size was 25 (other factors remain unchanged), the interval for $\mu$ would

An auto manufacturer wants to estimate the annual income of owners of a particular model of automobile. A random sample of 200 current owners is taken. The population standard deviation is known. Which Excel function would not be appropriate to use to construct a confidence interval estimate?

The manager of Hudson Auto Repair wants to advertise one price for an engine tune-up, with parts included. Before he decides the price to advertise, he needs a good estimate of the average cost of tune-up parts. A sample of 20 customer invoices for tune-ups has been taken and the costs of parts, rounded to the nearest dollar, are listed below.Provide a 90% confidence interval estimate of the mean cost of parts per tune-up for all of the tune-ups performed at Hudson Auto Repair. We will assume this population to be normally distributed.

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers revealed an average age of 28 years with a standard deviation of 10 years. Determine a 95% confidence interval estimate for the average age of all his customers. Assume the population of customer ages is normally distributed.

A newspaper wants to estimate the proportion of Americans who will vote for Candidate A. A random sample of 1000 voters is taken. Of the 1000 respondents, 526 say that they will vote for Candidate A. Which Excel function would be used to construct a confidence interval estimate?

The manager of a department store wants to determine what proportion of people who enter the store use the store's credit card for their purchases. What size sample should he take so that at 99% confidence the error will not be more than 8%?