Question

These are two hypotheses with the two samples drawn independently from 2 normally distributed distributions.

Ho: µ 1- µ2= 0

Ha: µ 1- µ2not equal to 0

µ 1 = 65

µ2= 76

Pop standard deviation= 5

Pop standard deviation= 4

n1= 25

n2=30

Test whether the population means differ at the 1% significance level.

Answer 1

ho: there is no significant difference in the mean between the two samples. u1 = u2
h1: there is a significant difference in the mean between the two samples. u1 =/= u2

	SAMPLE 1	SAMPLE 2
n=	25	30
mean=	65.00	76.00
s=	5.0000	4.0000
s^2/n	1.0000	0.5333

test statistic, t = (Xbar1 - Xbar2) / sqrt(s1^2/n1 + s2^2/n2)
t = (65 - 76) / sqrt(1+0.5333)
t = -8.8834

df = (s1^2/n1 + s2^2/n2)^2 / ((s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1))
df = (1+0.5333)^2 / ( 1^2/(25-1) + 0.5333^2/(30-1) )
df = 46

alpha=   0.01

p-value = 2*(1-P(T<|t|)
p-value = 2*(1-P(T<abs(-8.8834))
p-value = T.DIST.2T(abs(-8.8834),46)
p-value = 1.52795E-11 = 0.000

With t(46) = -8.8834, p<1%, i reject null hypothesis at 5% level of significance and conclude that there is a significant difference in the mean between the two samples. u1 =/= u2