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 or P-value method as indicated.

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 0.05 significance level to test the claim that the mean response time for company A is significantly different from the mean response time for company B. Use the P-value method of hypothesis testing.

Two-Sample T-Test
Sample N Mean StDev
A 50 7.6 1.4
B 50 6.9 1.7
Difference = mu (1) - mu (2)
Estimate for difference: 0.7
T-Test of difference = 0 (vs not =): T-Value = 2.248 P-Value = 0.027 DF = 94

At the 5% significance level, there is enough evidence to support the claim that the mean response time for company A is different from the mean response time for company B.

At the 5% significance level, there is not enough evidence to support the claim that the mean response time for company A is different from the mean response time for company B.

Answer 1

For the testing problem,

The value of the test statistic T = 2.248

and P-value = 0.027

Since p-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that

At the 5% significance level, there is enough evidence to support the claim that the mean response time for company A is different from the mean response time for company B.