Question

Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use the traditional method. 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 0.02 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 traditional method of hypothesis testing. ) Write the test statistic

please show all work

Answer 1

Let X1 and X2 be random variables for response times of companies A and B.

Given n1 = n2 = 50

To test if the mean response time are equal.

Let,

We have sample standard deviation only, so we will use t-test for two sample means.

Standard Error SE(X1-X2)

SE(X1-X2) = = 0.311

Degrees of freedom

df

= 0.00935 / 3.136*10^-5 + 6.818*10^-5 = 0.00935/9.954*10^-5 = 93.93

t-statistic

t = (X1-X2) / SE(X1-X2) = 7.6-6.9 / 0.311 = 2.25

p-value

For t = 2.25 and df = 93.93, p value is 0.0267

As p > 0.020, we do not have strong evidence against null hypothesis hence we conclude that the mean response time for company A is the same as the mean response time for company B.