Question

Consider the hypothesis statement shown below using alphaαequals=0.050.05 and the data to the right from two independent samples. Upper H 0 : mu 1 minus mu 2 equals 0H0: μ1−μ2=0 Upper H 1 : mu 1 minus mu 2 not equals 0H1: μ1−μ2≠0 ​a) Calculate the appropriate test statistic and interpret the result. ​b) Calculate the​ p-value and interpret the result.

x overbarx1	equals=	231231	x overbarx2	equals=	209209
sigmaσ1	equals=	6565	sigmaσ2	equals=	5353
n1	equals=	4444	n2	equals=	3636

Answer 1

Given information:

=231 , =209

=65 , =53

n₁ =44 , n₂ = 36

Hypothesis :

Two tailed test.

Here population standar deviations are known so we have to use two sample z test.

Test statistic -

z = 1.6676

P-value -

P- value for this two tailed test is,

P-value = 2*P( z >1.6676)

P( z >1.6676) = 1- P( z < 1.6676)

Using excel function,. =NORMSDIST( z)

P( z<1.6676) = NORMSDIST( 1.6676) =0.9523

So P(z > 1.6676)= 1 - 0.9523 = 0.0477

P- value = 2*0.0477 = 0.0954

P-value = 0.0954

Decision about null hypothesis-

Rule - Reject null hypothesis if p-value less than significance level

Here = 0.05

It is observed that p-value (0.0954) greater than significance level

So fail to reject null hypothesis.

Conclusion-

There is sufficient evidence to conclude that there is difference between population means.