Conduct a two-sample test of means A company is researching the effectiveness of

Question

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.

Explanation / Answer

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

32.000 mean Old 18.000 mean New 14.000 mean difference (Old - New) 7.211 std. dev. 3.225 std. error 5 n 4 df

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