Question

A study compared taste ratings from three different methods for cooking old-fashioned, hot oatmeal. The three methods were 1) get the water boiling before you add the oatmeal, then add the oatmeal, and allow light boiling for 5 minutes; 2) soak the oatmeal overnight, and then begin boiling, and allow light boiling for 5 minutes; 3) simply add the oatmeal, add the water, and fire up the burner to achieve a boil, and allow light boiling for 5 minutes. The study assigned at random 25 breakfasters to each method. After consuming the oatmeal, each sampled person gave a taste rating to the breakfast consumed. (i) What are the hypotheses for evaluating whether the average taste ratings are different for the different cooking methods? (ii) What are the degrees of freedom associated with the F-test for evaluating these hypotheses? (iii) Suppose we test at the level alpha = 0.05, and we find that the p-value for this test is 0.0135. What is the conclusion of the test?

Among the answer choices that follow, CHOOSE THE BEST COMBINATIONS OF THE OPTIONS GIVEN IN (i) AND (ii) AND (iii).

Group of answer choices

a. (i) H_0: Method 1 Taste Rating = Method 2 Taste Rating = Method 3 Taste Rating H_A: Each one of the methods yields a different taste rating. (ii) dfG = 2, dfE = 72 (iii) We conclude that there is sufficient evidence that each one of the methods associates with a different taste rating.

b. (i) H_0: Method 1 Taste Rating = Method 2 Taste Rating = Method 3 Taste Rating H_A: At least one of the methods yields a taste rating different from the other two. (ii) dfG = 2, dfE = 72 (iii) We conclude that there is sufficient evidence that at least one of the methods associates with a different taste rating.

c. (i) H_0: Method 1 Taste Rating = Method 2 Taste Rating = Method 3 Taste Rating H_A: At least one of the methods yields a taste rating different from the other two. (ii) dfG = 3, dfE = 72 (iii) We conclude that there is sufficient evidence that at least one of the methods associates with a different taste rating.

d. (i) H_0: Method 1 Taste Rating ≠ Method 2 Taste Rating ≠ Method 3 Taste Rating H_A: At least two of the methods yields the same taste rating. (ii) dfG = 2, dfE = 72 (iii) We conclude that there is sufficient evidence that at least two of the methods associate with the same taste rating.

e. None of the above answers sets is correct.

Answer 1

From the given information above,

we know if p value is less than level of significance then we reject the null hypothesis.

Best appropriate option is ,

(i) H_0: Method 1 Taste Rating = Method 2 Taste Rating = Method 3 Taste Rating H_A: At least one of the methods yields a taste rating different from the other two. (ii) dfG = 2, dfE = 72 (iii) We conclude that there is sufficient evidence that at least one of the methods associates with a different taste rating.