Question

1. A researcher was interested in comparing the response times of two different cab companies. Companies A and B were each called at 50 randomly selected times. The calls to company A were made independently of the calls to company B. The response times for each call were recorded. The summary statistics were as follows:

	Company A	Company B
Mean response time	7.6 mins	6.9 mins
Standard deviation	1.4 mins	1.7 mins

                    

Use a 0.01 significance level to test the claim that the mean response time for company A is the same as the mean response time for company B. Use the P-value method of hypothesis testing.

      Solution:

Answer 1

A) The hypothesis are

H0 :     v/s H1 :

B) The decision rule :

The critical values are = Z_0.01/2 = -2.576 and Z_1-0.01/2 = 2.576

We reject null hypothesis if calculated value of z > critical value of z.

OR

p value = 2* p ( Z < z_cal )

We reject null hypothesis if p value < ( 0.01)

C) The test statistic value is

= -2.24

d) p value = 2 * p ( Z < -2.24 ) = 2 * 0.0125 = 0.025

e) Here p value < . Hence we reject null hypothesis.

The mean response time for company A is not the same as the mean response time for company B.