Sample T Test

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)

• (0.92, -0.96)

• (-1.44, -0.96)

• (-1.84, -0.56)

• (0.92, 1.48)

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, μA - μB 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 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, μTC - μST , 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.

To compare 2 dog-training programs, an obedience school trained 43 dogs using Program A and 41 dogs using Program B. For Program A, the average number of training hours required was 24.8 with a standard deviation of 3.1 hours. For Program B, the mean was 22.9 hours with a standard deviation of 3.3 hours. Is there a significant difference between the two programs?

• One-Sample Z Test for a Proportion

• One-Sample Z Test for a Mean

• Two-Sample T Test for the Difference in Means

• Two-Sample Z Test for the Difference in Means

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.

Mr. Bucher wants to see if studying technique #1 (T1) resulted in a greater student average test score that studying technique #2. Using the previously found alternate hypothesis, and a signifiance level of 5%, what is the results of the t-test?

• Since 0.193 < 0.05, I reject my null. There is significant evidence that studying technique #1 resulted in a higher average than studying technique #2.

• Since 0.193 > 0.05, I reject my null. There is significant evidence that studying technique #1 resulted in a higher average than studying technique #2.

• Since 0.193 > 0.05, I fail reject my null. There is significant evidence that studying technique #1 do not resulted in a higher average than studying technique #2.

• Since 0.193 > 0.05, I fail to reject my null. There is insufficient evidence that t1 is greater thatn t2

A Keebler sales rep claims that there are more chocolate chips in their cookie than in Chips Ahoy cookies.  You take a random sample of 20 Keebler cookies and find an average of 15.8 chips per cookie and a s= 3.7 chips. A random sample of 25 Chips Ahoy yields 14.2 chips per cookie and s=4.3 chips.
What is the result of the test

• Reject the H₀

• Fail to Reject the H₀

• Reject the H_a

• Fail to reject the H_a

A two-sample t-test for a difference in means was conducted to investigate whether defensive players on a football team can bench-press more weight, on average, than offensive players. The conditions for inference were met, and the test produced a test statistic of t = 1.083 and a p-value of 0.15. Based on the p-value and a significance level of 5% , which of the following is the correct conclusion?

• Reject the null hypothesis because 0.15 > 0.05. There is not convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• B) Reject the null hypothesis because 0.15 > 0.05. There is convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• C) Fail to reject the null hypothesis because 0.15 > 0.05. There is not convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• D) Fail to reject the null hypothesis because 0.15 > 0.05. There is convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• E) Fail to reject the null hypothesis because 0.15 > 0.05. There is convincing evidence that defensive players can bench-press the same amount of weight, on average, as offensive players.