2 Sample T-test and Interval Review

120 Brand X oil filters and 90 Brand Y oil filters were tested for milligrams of residue, with the following results. Find a 95% confidence interval for μY - μX.

• (0.96, 1.44)

• B) (0.92, -0.96)

• C) (-1.44, -0.96)

• D) (-1.84, -0.56)

• E) (0.92, 1.48)

Two types of flares are tested for their burning times (in minutes) and sample results are given.

• (3.8, 4.8)

• (-4.7, -3.9)

• (3.6, 5.0)

• (3.5, 5.1)

• (3.2, 5.4)

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)

• Based on this sample, 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.

• Based on this sample, 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 grocery store is interested in determining whether or not a difference exists between the shelf life of Tasty Choice doughnuts and Sugar Twist doughnuts. A random sample of 100 boxes of each brand was selected and the mean shelf life in days was determined for each brand. A 90% confidence interval for the difference of the means, μ_TC - μ_ST , was determined to be ( 1.4, 2.5).

• We know that 90% of Tasty Choice doughnuts last between 1.4 and 2.5 days longer than Sugar Twist doughnuts.

• We are 90% confident that a randomly selected box of Tasty Choice doughnuts will have a shelf life that is between 1.4 and 2.5 days longer than a randomly selected box of Sugar Twist doughnuts.

• Based on this sample, we are 90% confident that Sugar Twist doughnuts will last on average between 1.4 and 2.5 days longer than Tasty Choice doughnuts.

• We know that 90% of all random samples done on the population will show that the mean shelf life of Tasty Choice doughnuts is between 1.4 and 2.5 days longer than the mean shelf life of Sugar Twist doughnuts.

• Based on this sample, we are 90% confident that Tasty Choice doughnuts will last on average between 1.4 and 2.5 days longer than Sugar Twist doughnuts.

A researcher was interested in comparing the salaries of female and male employees of a particular company. Independent random samples of 8 female employees (sample 1) and 15 male employees (sample 2) yielded the following weekly salaries (in dollars). Determine a 98% confidence interval for the difference, μ₁ - μ₂ between the mean weekly salary of all female employees and the mean weekly salary of all male employees.

• (-$385, $164)

• (-$158, $382)

• (-$335, $111)

• (-$431, $208)

• E) (-$382, $158)

A researcher was interested in comparing the heights of women in two different countries. Independent random samples of 9 women from country A and 9 women from country B yielded the following heights (in inches). Determine a 90% confidence interval for the difference, μ_A - μ_B between the mean height of women in country A and the mean height of women in country B.

• (-0.27, 4.65)

• (-0.82, 5.20)

• (0.14, 4.24)

• (0.02, 4.36)

• (0.16, 4.22)

A philosophy professor wants to find out whether the mean age of the men in his large lecture class is equal to the mean age of the women in his classes. After collecting data from a random sample of his students, the professor tested the hypothesis H₀: μ_M = μ_W against the alternative H_A: μ_M ≠ μ_W. The P-value for the test was 0.003. Which is true?

• It is very unlikely that the professor would see results like these if the mean age of men was equal to the mean age of women.

• There is a 0.3% chance that the mean ages for the men and women are equal.

• There is a 99.7% chance that another sample will give these same results.

• There is a 0.3% chance that another sample will give these same results.

• There is a 0.3% chance that the mean ages for the men and women are different.

You could win a $1000 prize by tossing a coin in one of two games. To win Game A, you must get exactly 50% heads. To win Game B, you must get between 45% and 55% heads. Although which game you must play will be chosen randomly, then you may decide whether to toss the coin 20 times or 50 times. How many tosses would you choose to make?

• 20 tosses for either game.

• 50 tosses for either game.

• 20 tosses for A, 50 tosses for B.

• It does not matter.

• 50 tosses for A, 20 tosses for B.