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.
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.
D) Suppose α = 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?
1) 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.
2) 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.
3) 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.
4) 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.

D)1) There is no evidence of a difference in the variability of the amount of time required to reach a customer service representative between the two hotels.

Step-by-step explanation:

The claim is that there is evidence of a difference in the variability of the amount of time required to reach a customer service representative between the two hotels which is the

alternate hypothesis

The null hypothesis is the reverse of the alternate hypothesis

The null hypothesis is that there is not enough evidence of a difference in the variability of the amount of time required to reach a customer service representative between the two hotels.

Part A) H0: σ₁²-σ₂²= 0 against the claim Ha: σ₁²-σ₂²≠0

Part B) t= x1`-x2`/ sqrt ( s₁²/n₁ + s₂²/n₂)

t= 2.214- 2.0115/ sqrt ( 2.951657/20+ 3.57855/20)

t= 0.2025/ sqrt(0.14758285 + 0.1789275)

t= 0.2025/0.5714108

t= 0.3543860

Part C) for 2 tailed test the critical value of t is obtained by

t≥ t∝/2 ( d.f)= ± 2.024394

We look at the table with values 0.025 as ∝/2= 0.05/2= 0.025

in the degrees of freedom 38

The d.f = n1+n2-2= 20+20-2= 40-2= 38

Part D) Since the calculated value of t= 0.3543860 does not fall in the critical region t≥ t∝/2 ( d.f)= ± 2.024394 we conclude that H0 is true and accept the null hypothesis.

So option 1 is correct

1) There is no evidence of a difference in the variability of the amount of time required to reach a customer service representative between the two hotels.