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 8 11 6 5 5 6 7 7 14 13 Diet B 9 12 7 12 14 16 7 23 10 21 (a) Find t. (Give your answer correct to two decimal places.) -2.1 (ii) Find the p-value.

Answer 1

Number	B	A	Difference ( B - A )
	9	8	1	15.21
	12	11	1	15.21
	7	6	1	15.21
	12	5	7	4.41
	14	5	9	16.81
	16	6	10	26.01
	7	7	0	24.01
	23	7	16	123.21
	10	14	-4	79.21
	21	13	8	9.61
Total	131	82	49	328.9

To Test :-

H0 :-

H1 :-  

Test Statistic :-





t = 2.56

Test Criteria :-
Reject null hypothesis if
Critical value
= 2.56 > 1.8331
Result :- Reject null hypothesis

Part ii)
P - value = P ( t > 2.56 ) = 0.0153

Looking for the value t = 2.56 in t table across n - 1 = 9 degree of freedom