Question

1. Consider the hypothesis test Ho:ui= u2 against Hi: 417 42. Suppose that sample sizes are n1 = 13, N2 = 10 X1=4.7, x2=6.8, s1=2 and S2 =2.5. Assume that the data are randomly drawn from two independent Normal distributions

Answer 1

Given
X1 bar	4.7	X2 bar	6.8
S1	2	S2	2.5
n1	13	n2	10

b)

Hypothesis :
Ho:	μ1​ = μ2
Ha:	μ1​ not = μ2

i)

Test :
Sp^2	4.964285714	((n1-1)S1^2+(n2-1)S2^2)/(n1+n2-2)
t	-2.240777156	(X1 bar-X2 bar )/SQRT(Sp^2*(1/n1 + 1/n2))	Equal vriance

ii)

t Critical Value :
tc	2.079613845	T.INV.2T(alpha,df)	TWO
Rejction region:
ts	< for -	tc	TWO	To reject
ts	> for +	tc	TWO	To reject

iii)

Decision :
If
P value	<	α = 0.05	Reject H0
P value	>	α = 0.05	Do not reject

iv)

P value :
P	0.035978961	T.DIST.2T(ts,df)	TWO

P value = 0.036

P value < 0.05, rejcet H0

v)

There is enough evidence to conclude that population means are different at 5% significance level

c)

95% CI

α=	0.05
df	21	n1+n2-2

CI	Equal variance
tc	2.079613845	T.INV.2T(alpha,df)
Upper	-0.151038203	(X1 bar-X2 bar )+tc*Sp*SQRT(1/n1 + 1/n2)
Lower	-4.048961797	(X1 bar-X2 bar )-tc*Sp*SQRT(1/n1 + 1/n2)

CI = (-4.0490, -0.1510)

The confidence intarval does not include null hypothesis value (0), so, we reject H0 and there is enough evidence to conclude that claim is true