Exam 8: Interval Estimation

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

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.

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 $\mu$ at 96.6% confidence, the Z value to use is

A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is

A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks to their clients. A sample of the sales for 36 days revealed average daily sales of $200,000. Assume that the standard deviation of the population is known to be $18,000. a.Provide a 95% confidence interval estimate for the average daily sale. b.Provide a 97% confidence interval estimate for the average daily sale.

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

For the interval estimation of $\mu$ when $\sigma$ is known and the sample is large, the proper distribution to use is

Below you are given ages that were obtained by taking a random sample of 9 undergraduate students. Assume the population has a normal distribution. a.What is the point estimate of $\mu$ ? b.Determine the standard deviation. c.Construct a 90% confidence interval for the average age of undergraduate students. d.Construct a 99% confidence interval for the average age of undergraduate students. e. Discuss why the 99% and 90% confidence intervals are different.

The Highway Safety Department wants to study the driving habits of individuals. A sample of 81 cars traveling on the highway revealed an average speed of 67 miles per hour with a standard deviation of 9 miles per hour. a.Compute the standard error of the mean. b.Determine a 99% confidence interval estimate for the speed of all cars.

When the level of confidence decreases, the margin of error

A random sample of 53 observations was taken. The average in the sample was 90 with a variance of 400. a.Construct a 98% confidence interval for $\mu$ . b.Construct a 99% confidence interval for $\mu$ . c.Discuss why the 98% and 99% confidence intervals are different. d.What would you expect to happen to the confidence interval in Part a if the sample size was increased? Be sure to explain your answer.

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

A statistician employed by a consumer testing organization reports that at 95% confidence he has determined that the true average content of the Uncola soft drinks is between 11.7 to 12.3 ounces. He further reports that his sample revealed an average content of 12 ounces, but he forgot to report the size of the sample he had selected. Assuming the standard deviation of the population is 1.28, determine the size of the sample.

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

The Highway Safety Department wants to study the driving habits of individuals. A sample of 121 cars traveling on the highway revealed an average speed of 60 miles per hour with a standard deviation of 11 miles per hour. Determine a 95% confidence interval estimate for the speed of all cars.

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.

In a sample of 200 individuals, 120 indicated they are Democrats. Develop a 95% confidence interval for the proportion of people in the population who are Democrats.

As the sample size increases, the margin of error

A simple random sample of 144 items resulted in a sample mean of 1257.85 and a standard deviation of 480. Develop a 95% confidence interval for the population mean.

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.