A market analyst wants to know if the new website he designe

A market analyst wants to know if the new website he designed is showing increased page views per visit. Assume that the new website is website 1 and the old website is website 2. Test the hypothesis that the mean number of page views from the two websites is the same. Assume that the number of page views from each website follows a normal distribution.

Website 1                     website 2

N1= 90                          n2= 85

Y1= 7.6                         y2= 7.5

S1= 4.7                         s2= 4.8

T= 0.139

Calculate the p value of the statistic given that the approximation formula gives df= 171.9

Calculate the p value of the statistic using the rule that df= min(n1-1, n2-1)

What do you conclude at a= 0.10

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate Hypothesis, There Is Significance between them - H1: u1 != u2
Test Statistic
X(Mean)=7.6
Standard Deviation(s.d1)=4.7 ; Number(n1)=90
Y(Mean)=7.5
Standard Deviation(s.d2)=4.8; Number(n2)=85
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =7.6-7.5/Sqrt((22.09/90)+(23.04/85))
to =0.14
| to | =0.14
Critical Value
The Value of |t ?| with Min (n1-1, n2-1) i.e 84 d.f is 1.663
We got |to| = 0.13914 & | t ? | = 1.663
Make Decision
Hence Value of |to | < | t ? | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 0.1391 ) = 0.89
Hence Value of P0.1 < 0.89,Here We Do not Reject Ho, Yes it is same