Estimating the Difference in Two Population Means

Which of the following examples suggests a confidence interval for the difference between two independent means?

• What is the average height of 16 year old American males?

• How much taller are 16 year old American males than females?

• What is the average increase in height of American males between ages 13 and 16?

• Is the average height of 16 year old American males greater than 68 inches?

A researcher was interested in comparing the salaries of employees of a particular company that work in the HR and IT departments. Independent random samples of 8 HR employees and 15 IT employees yielded the weekly salaries shown in the table (in dollars). Construct a 98% confidence interval estimate of the difference in population mean weekly salary.

• (-$385, $164)

• (-$158, $382)

• (-$335, $111)

• (-$431, $208)

• (-$382, $158)

A researcher was interested in comparing the salaries of employees of a particular company that work in the HR and IT departments. Independent random samples of 8 HR employees and 15 IT employees yielded the weekly salaries shown in the table (in dollars). Which inference method would make the most sense based on the information given?

• Two-sample pooled z-interval for means

• Two-sample pooled t-interval for means

• Matched pairs t-interval

• Two-sample z-interval for means

• Two-sample t-interval for means

A survey was conducted to determine the difference in gasoline mileage for two types of trucks. A random sample was taken for each model of truck, and the mean gasoline mileage, in miles per gallon, was calculated. A 98% confidence interval for the difference in the mean mileage for model A trucks and the mean mileage for model B trucks, μ_{A -} μ_B was determined to be (2.6, 4.5). Which of the following would be the most appropriate conclusion statement?

• We are 98% confident that the average mileage for model B trucks is between 2.6 and 4.5 miles per gallon higher than the average mileage for model A trucks.

• We know that 98% of model A trucks get mileage that is between 2.6 and 4.5 miles per gallon higher than model B trucks.

• We are 98% confident that the average mileage for model A trucks is between 2.6 and 4.5 miles per gallon higher than the average mileage for model B trucks.

• We are 98% confident that a randomly selected model A truck will get mileage that is between 2.6 and 4.5 miles per gallon higher than a randomly selected model B truck.

• We know that 98% of all random samples done on the population of trucks will show that the average mileage for model A trucks is between 2.6 and 4.5 miles per gallon higher than the average mileage for model B trucks.

A survey was conducted to determine the difference in gasoline mileage for two types of trucks. A random sample was taken for each model of truck, and the mean gasoline mileage, in miles per gallon, was calculated. A 98% confidence interval for the difference in the mean mileage for model A trucks and the mean mileage for model B trucks, μ_{A -} μ_B was determined to be (2.6, 4.5). Which of the following would be the point estimate of the confidence interval?

• 1.55

• Cannot determine from the information given.

• 3.55

• 1.9

• 0.95

A survey was conducted to determine the difference in gasoline mileage for two types of trucks. A random sample was taken for each model of truck, and the mean gasoline mileage, in miles per gallon, was calculated. A 98% confidence interval for the difference in the mean mileage for model A trucks and the mean mileage for model B trucks, μ_{A -} μ_B was determined to be (2.6, 4.5). Which of the following would be the margin of error for the confidence interval?

• 1.55

• Cannot determine from the information given.

• 3.55

• 1.9

• 0.95

A study was conducted to determine the retirement ages for individuals working in the private sector versus individuals working in the public sector. The researcher obtained data from a random sample of 216 working individuals. The results are shown. Construct a 90% confidence interval for the difference in population mean retirement age.

• (-$4.91, -$1.09)

• (-$4.91, -$1.09)

• (-$5.28, -$0.72)

• (-$4.49, -$1.51)

What type of test?
It is thought that the average penny is older than the average quarter. The average age of a sample of 50 pennies was 8.72 years with a s = 0.73 years and the average age of 50 quarters was 6.78 years with a s = 0.99 years.

• Two-sample z-interval for means

• Two-sample t-interval for means

• Matched pairs t-interval

• Two-sample pooled z-interval for means

Do high school seniors with part-time jobs spend less time doing homework per week, on average, than seniors without part-time jobs? For a random sample of 45 seniors with part-time jobs, the mean amount of homework time is 4.2 hours with a standard deviation of 3.8 hours. For a random sample of 45 seniors without part time jobs, the mean amount of homework time is 5.8 hours with a standard deviation of 4.9 hours. Assuming the conditions are met, which of the following is the correct standard error for a 95% confidence interval for a difference in the population means?

Answer explanation

Be careful to not confuse the means with the standard deviations in this expression.

Do high school seniors with part-time jobs spend less time doing homework per week, on average, than seniors without part-time jobs? For a random sample of 45 seniors with part-time jobs, the mean amount of homework time is 4.2 hours with a standard deviation of 3.8 hours. For a random sample of 45 seniors without part time jobs, the mean amount of homework time is 5.8 hours with a standard deviation of 4.9 hours. Assuming the conditions are met, which of the following is the correct margin of error for a 95% confidence interval for a difference in the population means?

• 0.924

• 1.989

• 1.838

• -1.6

• 82.867

Answer explanation

Be careful to not confuse the means with the standard deviations in this expression.