Question

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method.

A study was done on body temperatures of men and women. Here are the sample statistics for the men: x1 = 97.55oF, s1 = 0.83oF, n1 = 11, and for the women: x2 = 97.31oF, s2 = 0.65oF, n2 = 59. Use a 0.06 significance level to test the claim that µ1 > µ2.

Answer 1

Given
X1 bar	97.55	X2 bar	97.31
S1	0.83	S2	0.65
n1	11	n2	59

Hypothesis :		α=	0.06
		df	68	n1+n2-2
Ho:	μ1​ = μ0
Ha:	μ1​ > μ0
t Critical Value :
tc	1.574557904	T.INV(1-D1,9)	RIGHT
ts	>=	tc	RIGHT	To reject
Test :
Sp^2	0.461676471	((n1-1)S1^2+(n2-1)S2^2)/(n1+n2-2)
t	1.075513087	(X1 bar-X2 bar )/SQRT(Sp^2*(1/n1 + 1/n2))	Equal vriance
P value :
P value	0.183414112	T.DIST.RT(ts,df)	RIGHT
Decision :
P value	>	α	Do not reject

there is not enough evidence to conclude that the mean body temperatures of men greater than women at 6% significance level