Exam 8: Interval Estimation

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

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?

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.

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

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

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 16 pieces of carry-on luggage was weighed. The average weight was 20 pounds. Assume that we know the standard deviation of the population to be 8 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.

A quality control technician is checking the weights of a product. She takes a random sample of 8 units and weighs each unit. The observed weights are shown below. Assume the population has a normal distribution. Provide a 95% confidence interval for the mean weight of the units.

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

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.

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?

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 $\mu$

An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the

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. If we want to provide a 95% confidence interval for the SAT scores, the degrees of freedom for reading the critical values of "t" statistic is

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

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. If we want to determine a 95% confidence interval for the average hourly income, the value of "t" statistics is

Using an $\alpha$ = 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

A university planner is interested in determining the percentage of spring semester students who will attend summer school. She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school. a.Construct a 95% confidence interval estimate for the percentage of spring semester students who will return to summer school. b.Using the results of the pilot study with a 0.95 probability, how large of a sample would have to be taken to provide a margin of error of 3% or less?

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?

A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is

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.