Conduct a twosample test of means A company is researching t

Conduct a two-sample test of means

A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected and their times (in seconds) to access the website with the old and new designs were recorded. The results follow.

a 30 15
b 45 20
c 25 10
d 32 25
e 28 20

Let ? = 0.05. Is the mean time to access the new website design shorter, or is (time for the old design - time for the new design) greater than zero? Express your answer in terms of the null hypothesis.

Solution

Let mu_d be the mean difference between time for the old design and time for the new design

The test hypothesis:

Ho: mu_d = 0 (i.e. null hypothesis)

Ha: mu_d>0 (i.e. alternative hypothesis)

The test statistic is

t= mean difference/(s/vn)

=14/(7.211/sqrt(5))

=4.34

The degree of freedom =n-1=5-1=4

It is a right-tailed test.

Given a=0.05, the critical value is t(0.05, df=4) =2.13 (from student t table)

The rejection region is if t>2.13, we reject the null hypothesis.

Since t=4.34 is larger than 2.13, we reject the null hypothesis.

So we can conclude that the mean time to access the new website design is shorter