Question

Researchers are interested in whether there is a difference in happiness levels between people that live on the West Coast and people that live on the East Coast. A simple random sample of people were selected from each coast to take an assessment of their happiness. Scores on the happiness assessment range from 1-20.

The happiness scores for the individuals assessed are below.

East Coast Happiness Scores	West Coast Happiness Scores
9.7, 18.8, 19.9, 10.1, 8.9, 15.0, 16.4, 10.1, 11.0, 19.5, 16.6, 16.1, 19.0	12.2, 9.6, 20.0, 19.3, 14.4, 16.3, 15.3, 18.0, 18.5, 19.4

Complete an appropriate significance test the compare to happiness levels. What is the P-value of this test?

Answer 1

Given:

The happiness scores for the individuals assessed are below.

East Coast Happiness Scores	West Coast Happiness Scores
9.7, 18.8, 19.9, 10.1, 8.9, 15.0, 16.4, 10.1, 11.0, 19.5, 16.6, 16.1, 19.0	12.2, 9.6, 20.0, 19.3, 14.4, 16.3, 15.3, 18.0, 18.5, 19.4

For east coast happiness scores :

1 = 14.7, n1 = 13, s1 = 4.1691

For west coast happiness scores :

2 = 16.3, n2 = 10, s2 = 3.4374

Hypothesis test:

The null and alternative hypothesis is

Ho : 1 = 2

Ha : 1 2 (This is a two tailed test)

Test statistics is

So P-value = 0.3249