Twenty laboratory mice were randomly divided into two groups of 10. Each group w

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 = 0.05 level of significance? Assume normality. (Use Diet B - Diet A.)

(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.

Explanation / Answer

Data set for Diet B-Diet A=2,1,-7,7,15,-4,5,8,-5,-1

Mean=2.1

standard deviation of data=6.79

Hence standard dev of mean=6.79/sqrt(10)=2.147

t value=t*=2.1/2.147=0.978

Hence t(0.025,9)=2.262

p=0.3536

Hence as t*<t,we fail to reject H0,there is no sinificant evidence that diet B had a greater weight gain.

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