Question

A market research firm is testing whether a new color scheme for a client's website causes...

A market research firm is testing whether a new color scheme for a client's website causes more time be spent reading the site. To test this theory, the firm randomly selected 20 of the pages on their client's site, and used the new color scheme . on Saturday. The old color scheme was restored on Sunday. The average time in minutes that people spent on each of the 20 pages was recorded. Assume that both of the populations are normally distributed.

The firm tests the paired data, where α=0.05, in order to evaluate the claim that the true mean difference in the times between the old color scheme and the new color scheme is significantly different from zero.

Here, H0:μd=0, Ha:μd≠0, which is a two-tailed test.

Pair Old Scheme New Scheme
1   2   2.5
2   1.8   2.2
3   0.9   1
4   1.4   1.7
5   1.9   2.9
6   1.6   3.1
7   1   1.7
8   2.3   2.4
9   2.2   2.5
10   1.1   1.6
11   1.4   2.9
12   2.6   2.9
13   0.7   0.7
14   2.1   1.9
15   2.2   2.9
16   2.4   3.2
17   0.8   0.7
18   2.2   1.9
19   1.4   1
20   2.3   2.3

The average times (in minutes) people spent looking at each page under each color scheme are provided in the above data set.

Use Excel to test the paired data and evaluate the claim that the true mean difference is significantly different from zero. For each pair, subtract the new scheme time from the old scheme time. Identify the test statistic, t, and p-value from the Excel output.

• Round your test statistic to two decimal places and your p-value to three decimal places.

test statistic = , p-value =