Question

3. A researcher believes that community B has a lower income than community A. Forty people are surveyed in each of the two communities regarding their income. In place A, the mean among the 40 individuals is 62 (given in thousands; you can ignore the ‘thousands’ and just use ‘61’), and the variance is 95; in place B, the mean among the 40 surveyed is 59, and the variance is 100.   Test the null hypothesis that the two communities have equal incomes. Use alpha = 0.05. State the null and alternative hypotheses, find the test statistic, compare it with the critical value, make a decision, and find the p-value.

Answer 1

Given
X1 bar	62	X2 bar	59
S1	9.75	S2	10
n1	40	n2	40

Hypothesis :		α=	0.05
		df	78	n1+n2-2
Ho:	μ1​ = μ2
Ha:	μ1​ > μ2
t Critical Value :
tc	1.664624645	T.INV(1-alpha,df)	RIGHT
ts	>=	tc	RIGHT	To reject
Test :
Sp^2	97.5	((n1-1)S1^2+(n2-1)S2^2)/(n1+n2-2)
t	1.358732441	(X1 bar-X2 bar )/SQRT(Sp^2*(1/n1 + 1/n2))	Equal vriance
P value :
P value	0.089073865	T.DIST.RT(ts,df)	RIGHT
Decision :
P value	>	α	Do not reject

Decision:

P value > 0.05, Do not reject H0

There is not enough evidence that community B has a lower income than community A at 5% significance level