Calculate the test statistic (t) and p-value for each sample mean (note: population variance is unknown): 1) H0: µ ≥ 200 versus H1: µ < 200, α = 0

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Calculate the test statistic (t) and p-value for each sample mean (note: population variance is unknown):

1) H₀: µ ≥ 200 versus H₁: µ < 200, α = 0.05, x (mean) = 198, s = 5, n = 25

A) (t = -2.00, p-value = 0.0285)

B) (t = 2.00, p-value = 0.0285)

C) (t = -2.00, p-value = 0.9850)

D) (t = -2.00, p-value = 0.0852)

 

2) The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 ounces with a standard deviation of 0.41 ounces. The calculated test statistic is t = -2.28 (left tail test) and the corresponding p-value = 0.018.

 

Based on the results above, is the sample mean (17.78 ounces) smaller than the specification (18 ounces) at the 0.05 level of significance? (Check one of the following responses):

 

A. Yes, the sample mean is significantly smaller than the specification at 0.05 level of significance.

B. No, the sample mean is not significantly smaller than the specification at 0.05 level of significance.

C. Yes, the p-value is greater than the alpha level.

D. No, the p-value is lower than 0.01

 

3) Which of the following comparisons would use a "paired t-test"?

 

A.   Fifteen retirees with diagnosed hypertension are assigned a program of diet, exercise, and meditation. A baseline measurement of blood pressure is taken before the program begins and again after 2 months. Was the program effective in reducing blood pressure of the participants after analyzing the mean blood pressure before the program compared to mean blood pressure after the program?

B.   Comparing average GPA of male undergraduate students vs. average GPA of female undergraduate students

C.  Comparing average age of juniors vs. average age of seniors.

D.  Comapring the average GPA of economics majors, biology majors, and computer science majors.

 

4) Which of the following comparisons would use a t-test comparing two independent groups?

 

A.   Fifteen retirees with diagnosed hypertension are assigned a program of diet, exercise, and meditation. A baseline measurement of blood pressure is taken before the program begins and again after 2 months. Was the program effective in reducing blood pressure of the participants after analyzing the mean blood pressure before the program compared to mean blood pressure after the program?

B.   Comparing average GPA of male undergraduate students vs. average GPA of female undergraduate students

C.  Comparing average age of freshman, sophomores, juniors, and seniors.

D.  Comapring the average GPA of economics majors, biology majors, and computer science majors.