Question

If two independent populations are sampled and known :
Sample 1 : n1=80, ?̅ 1=104, σ1=8.4
Sample 2 : n2 = 70 ?̅ 2=106 σ2 =7.6
test the hypotesis H0 : μ1=μ2 vs H1: μ1≠μ2 pada α=0.05 and give conclussions.

Note: no handwritten answer would be very appreciated. thanks.

Answer 1

from the above information

Sample 1 : n1=80, ?̅ 1=104, σ1=8.4
Sample 2 : n2 = 70 ?̅ 2=106 σ2 =7.6

test the hypotesis

H0 : μ1=μ2 vs H1: μ1≠μ2

The test satistic formula is

I have used z test becouse the n1,n2>30 and also the standard deviation is knoen

z=(104-106)/root((8.4)^2/80+(7.6)^2/70)

z=-1.530718

critical value of z=1.96

also the p value= 0.1260

the calculated z< table value of x

or the p value is > level of significance

so we fail to reject Ho

i.e μ1=μ2