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. A customer is randomly sent to one of two different websites, offering the same products, but with different designs. The table shows the data from five randomly chosen customers from each website. Assume that the data come from a distribution that is normally distributed. Find a 95% confidence interval for the mean difference, in page views from the two websites using the pooled degrees of freedom.

Website 1

10

3

13

9

6

Website 2

11

13

2

4

5

Solution

The degree of freedom =n1+n2-2=5+5-2=8

Given a=1-0.95=0.05, t(0.025, df=8) =2.31 (from student t table)

So the lower bound is

(xbar1-xbar2) -t*sqrt(s1^2/n1+s2^2/n2)

=(8.2-7) -2.31*sqrt(3.83^2/5+4.74^2/5)

=-5.09546

So the upper bound is

(xbar1-xbar2) +t*sqrt(s1^2/n1+s2^2/n2)

=(8.2-7) +2.31*sqrt(3.83^2/5+4.74^2/5)

=7.49546