Question

A USA based cable broadband company wants to compare the average customer satisfaction scores between its east coast and west coast customer bases.
The customer survey asks for a score between 1 and 5, with 1 being poor and 5 being excellent.

174 east coast customers are surveyed, and the sample mean is 3.51 with a sample standard deviation of 0.51. For the west coast, 355 customers are surveyed, and the sample mean is 3.24 with a sample standard deviation of 0.52.

Let east coast customers be population 1 and west coast customers be population 2.

a) The company wants to see if east coast and west coast customers have different average scores. Pick the correct null and alternative hypothesis.

b) The test statistic for this test is -5.65. How would you obtain the p-value for this test based on this test statistic?

c) Say the p-value is approximately 0. what can you conclude?

Answer 1

a)we have to test,

H0 : 1=2 v/s

H1 : 12

b)Given test is two sided test,

And t statistic=-5.65

degrees of freedom = 174+355-2= 527

using excel for p value as,

=T.DIST.2T(-5.65,527)=2.18131e-8

i.e. p value is 0

C) p value is 0.

We reject the null hpotheis.

i.e.

​east coast and west coast customers have different average scores.