Exam 8: Interval Estimation

Computer Services, Inc. wants to determine a confidence interval for the average CPU time of their teleprocessing transactions. A sample of 64 transactions yielded a mean of 6 seconds with a standard deviation of 0.8 seconds. Determine a 98% confidence interval for the average CPU time.

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.

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. If the sample mean is 1,858 KWH, the 95% confidence interval estimate of the population mean is

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 value of the margin of error at 95% confidence is

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. With a .95 probability, the sample mean will provide a margin of error of

In order to determine how many hours per week freshmen college students watch television, a random sample of 256 students was selected. It was determined that the students in the sample spent an average of 14 hours with a standard deviation of 3.2 hours watching TV per week. a. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week. Assume that a sample of 62 students was selected with the same mean and the standard b. deviation). Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week.

A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The standard deviation of the population is known to be $66. a. Is it necessary to know anything about the shape of the distribution of the account balances in order to make an interval estimate of the mean of all the account balances? Explain. b. Find the standard error of the mean. c. Give a point estimate of the population mean. d. Construct a 80% confidence interval estimates for the mean. e. Construct a 95% confidence interval for the mean.

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 the confidence coefficient is reduced to 0.9, the standard error of the mean

A random sample of 121 checking accounts at a bank showed an average daily balance of $300 and a standard deviation of $44. Develop a 95% confidence interval estimate for the mean of the population.

A statistician selected a sample of 16 accounts receivable and determined the mean of the sample to be $5,000 with a standard deviation of $400. He reported that the sample information indicated the mean of the population ranges from $4,739.80 to $5,260.20. He neglected to report what confidence coefficient he had used. Based on the above information, determine the confidence coefficient that was used. Assume the population has a normal distribution.

Whenever using the t distribution for interval estimation when the sample size is very small), we must assume that

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

Using an α = 0.04 a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion

The following random sample from a population whose values were normally distributed was collected. 10 8 11 11 The 95% confidence interval for μ is

A coal company wants to determine a 95% confidence interval estimate for the average daily tonnage of coal that they mine. Assuming that the company reports that the standard deviation of daily output is 200 tons, how many days should they sample so that the margin of error will be 39.2 tons 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. If the sample size was 100 other factors remain unchanged), the interval for μ would

In developing an interval estimate, if the population standard deviation is unknown

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

For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is

In order to determine the summer unemployment rate among college students, a pilot sample was taken; and it was determined that ten percent of the individuals in the sample were unemployed. Using the results of the pilot study and a 95% confidence, what size sample would be required to estimate the proportion of unemployed college students if we want the margin of error not to exceed 3 percent?