Question

Listed below are brain volumes (cm3 ) of twins.

First Born	1005	1035	1281	1051	1034	1079	1104	1439	1029	1160
Second Born	963	1027	1272	1079	1070	1173	1067	1347	1100	1204

Test the claim at the 5% significance level that the brain volume for the first born is different from the second-born twin.

(a) State the null and alternative hypotheses.

(b) Find the critical value and the test statistic.

(c) Should H0 be rejected at the 5% significance level? Make a conclusion.

(d) Construct a 95% confidence interval for the paired difference of the population means

Answer 1

	First born ( X )		Second Born ( Y )
	1005	13618.89	963	27955.84
	1035	7516.89	1027	10650.24
	1281	25376.49	1272	20107.24
	1051	4998.49	1079	2621.44
	1034	7691.29	1070	3624.04
	1079	1823.29	1173	1831.84
	1104	313.29	1067	3994.24
	1439	100679.29	1347	47002.24
	1029	8593.29	1100	912.04
	1160	1466.89	1204	5446.44
Total	11217	172078.1	11302	124145.6

To Test :-

H₀ :-  

H₁ :-  

Test Statistic :-


t = -0.1482
Test Criteria :-
Reject null hypothesis if


DF = 17
Critical value   

Result :- Fail to Reject Null Hypothesis

Conclusion - Accept Null Hypothesis

There is no sufficient evidence to support the claim that the brain volume for the first born is different from the second-born twin.

Confidence interval :-


Lower Limit =
Lower Limit = -129.5518
Upper Limit =
Upper Limit = 112.5518
95% Confidence interval is ( -129.5518 , 112.5518 )