Question

A company is trying to select an Internet provider and to decide which one is better. It decides to try downloading some documents from different WebSites and comparing the downloading times in all cases.

Provider A Data: 17, 29, 18, 14, 21, 25, 22, 29, 34, 18

Provider B Data: 21, 38, 15, 19, 22, 30, 31, 37, 36, 20

a. Can the company conclude that A is different from and better than B at a 5% level of significance?

b. Will the results stay the same at the 1% level of significance?

Answer 1

Let us denote

d : difference of download times by Provider A and Provider B

i.e. d = download times by Provider A - download times by Provider B

To test against

Here

sample mean of difference

sample standard deviation of difference

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic =

and p-value

a) Since p-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that downloading time by provider A is significantly less than by Provider B.

b) Since p-value < 0.01, so we reject H₀ at 1% level of significance and we can conclude that downloading time by provider A is significantly less than by Provider B.