Question

Twenty laboratory mice were randomly divided into two groups of 10. Each group was fed according to a prescribed diet. At the end of 3 weeks, the weight gained by each animal was recorded. Do the data in the following table justify the conclusion that the mean weight gained on diet B was greater than the mean weight gained on diet A, at the α = 0.05 level of significance? Assume normality. (Use Diet B - Diet A.)

Diet A	7	12	10	6	14	11	5	13	7	9
Diet B	22	12	19	20	10	7	9	6	13	22

(a) Find t. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer correct to four decimal places.)

(b) State the appropriate conclusion.

Reject the null hypothesis, there is significant evidence that diet B had a greater weight gain.

Reject the null hypothesis, there is not significant evidence that diet B had a greater weight gain.    

Fail to reject the null hypothesis, there is significant evidence that diet B had a greater weight gain.

Fail to reject the null hypothesis, there is not significant evidence that diet B had a greater weight gain.

Answer 1

(a) Find t.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

Dbar = 4.6

Sd = 8.1131

n = 10

t = (4.6 - 0)/[ 8.1131/sqrt(10)]

t = 1.7930

t = 1.79

(ii) Find the p-value.

Df = n - 1 = 10 - 1 = 9

P-value = 0.0535

(b) State the appropriate conclusion.

P-value > α = 0.05

So, we fail to reject the null hypothesis

Fail to reject the null hypothesis; there is not significant evidence that diet B had a greater weight gain.