The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal. t-Test: Two-Sample Assuming Unequal Variances
Hotel 1 Hotel 2
Mean 2.214 2.0115
Variance 2.951657 3.57855
Observations 20 20
Hypothesized Mean Difference 0
df 38
t Stat 0.354386
P(T<=t) one-tail 0.362504
t Critical one-tail 1.685953
P(T<=t) two-tail 0.725009
t Critical two-tail 2.024394
a) State the null and alternative hypotheses for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels.
b) What is the value of the test statistic for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels? Explain how you obtain your answer.
c) What is the critical value for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels at the 5% level of significance? Explain how you obtain your answer.
d) Suppose ? = 0.05. Which of the following represents the correct conclusion for a test on a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels? Show how you obtain your answer.
A) There is no evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels.
B) There is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels.
C) There is no evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same.
D) There is evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same.