Exam 8: Interval Estimation

A sample of 60 students from a large university is taken. The average age in the sample was 22 years with a standard deviation of 6 years. Construct a 95% confidence interval for the average age of the population.

Exhibit 8-2 A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph. -Refer to Exhibit 8-2. If we are interested in determining an interval estimate for μ at 96.6% confidence, the Z value to use is

A random sample of 81 students at a local university showed that they work an average of 60 hours per month with a standard deviation of 18 hours. Compute a 95% confidence interval for the mean of the population.

A local health center noted that in a sample of 400 patients 80 were referred to them by the local hospital. a. Provide a 95% confidence interval for all the patients who are referred to the health center by the hospital. b. What size sample would be required to estimate the proportion of hospital referrals with a margin of error of 0.04 or less at 95% confidence?

Exhibit 8-3 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 population of checkout times is one minute. -Refer to Exhibit 8-3. The standard error of the mean equals

Exhibit 8-1 In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. -Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is

In a random sample of 400 registered voters, 120 indicated they plan to vote for Candidate A. Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Candidate A.

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 53 customers revealed an average age of 28 years with a standard deviation of 4 years. Determine a 98% confidence interval estimate for the average age of all his customers.

A random sample of 49 lunch customers was taken at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 45 minutes with a standard deviation of 14 minutes. a. Compute the standard error of the mean. b. With a .95 probability, what statement can be made about the size of the margin of error? c. Construct a 95% confidence interval for the true average amount of time customers spent in the restaurant. d. With a .95 probability, how large of a sample would have to be taken to provide a margin of error of 2.5 minutes or less?

A sample of 144 cans of coffee showed an average weight of 16 ounces. The standard deviation of the population is known to be 1.4 ounces. a. Construct a 68.26% confidence interval for the mean of the population. b. Construct a 97% confidence interval for the mean of the population. c. Discuss why the answers in Parts a and b are different.

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is

A researcher is interested in determining the average number of years employees of a company stay with the company. If past information shows a standard deviation of 7 months, what size sample should be taken so that at 95% confidence the margin of error will be 2 months or less?

In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is

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. At 95% confidence, the size of the margin of error is

It is known that the variance of a population equals 1,936. A random sample of 121 has been taken from the population. There is a .95 probability that the sample mean will provide a margin of error of

A new brand of chocolate bar is being market tested. Four hundred of the new chocolate bars were given to consumers to try. The consumers were asked whether they liked or disliked the chocolate bar. You are given their responses below. Response Frequency Liked 300 Disliked 100 400 a. What is the point estimate for the proportion of people who liked the chocolate bar? b. Construct a 95% confidence interval for the true proportion of people who liked the chocolate bar. c. With a .95 probability, how large of a sample needs to be taken to provide a margin of error of 3% or less?

A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for μ is

If the population standard deviation of the lifetime of washing machines is estimated to be 900 hours, how large a sample must be taken in order to be 97% confident that the margin of error will not exceed 100 hours?

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

Exhibit 8-5 A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. -Refer to Exhibit 8-5. The "t" value for this interval estimation is