Exam 8: Interval Estimation

A local university administers a comprehensive examination to the recipients of a B.S. degree in Business Administration. A sample of 5 examinations is selected at random and scored. The scores are shown below. a.Compute the sample mean and the standard deviation. b.Determine the margin of error at 95% confidence. c.At 95% confidence, determine an interval for the mean of the population. At 98% confidence, determine an interval for the mean of the population.

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?

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

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?

In general, higher confidence levels provide

It is known that the variance of a population equals 1296. A random sample of 144 observations is going to be taken from the population. a.With a 0.95 probability, what statement can be made about the size of the margin of error? b.With a 0.95 probability, how large of a sample would have to be taken to provide a margin of error of 6 or less?

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. The 96.6% confidence interval for $\mu$ is

In determining the sample size necessary to estimate a population proportion, which of the following information is not needed?

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

You are given the following information obtained from a random sample of 6 observations. Assume the population has a normal distribution. a.What is the point estimate of $\mu$ ? b.Construct an 80% confidence interval for $\mu$ . c.Construct a 98% confidence interval for $\mu$ . d.Discuss why the 80% and 98% confidence intervals are different.

We are interested in conducting a study in order to determine what percentage of voters of a state would vote for the incumbent governor. What is the minimum size sample needed to estimate the population proportion with a margin of error of 0.05 or less at 95% confidence?

The average score of a sample of 87 senior business majors at UTC who took the Graduate Management Admission Test was 510 with a standard deviation of 36. Provide a 98% confidence interval for the mean of the population.

When constructing a confidence interval for the population mean and the standard deviation of the sample is used, the degrees of freedom for the t distribution equals

When the level of confidence decreases, the margin of error

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

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. With a 0.95 probability, the margin of error is approximately

The z value for a 97.8% confidence interval estimation is

Choo Choo Paper Company produces papers of various thickness. A random sample of 256 cuts had a mean thickness of 30.3 mils with a standard deviation of 4 mils. Develop a 95% confidence interval for the mean thickness of the population.

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 95% confidence interval for the true average checkout time (in minutes) is