The customer service group at the national headquarters of an automotive manufac

ID: 3181898 • Letter: T

Question

The customer service group at the national headquarters of an automotive manufacturing company sends out a customer satisfaction survey shortly after a vehicle purchase. Customers are asked to rate their overall satisfaction with the buying experience as "Extremely satisfied", "Somewhat satisfied", "Somewhat dissatisfied" or "Extremely dissatisfied." In the past, 42% of customers have responded "Extremely satisfied", 30% have responded "Somewhat satisfied", 22% have responded "Somewhat dissatisfied", and 6% have responded "Extremely dissatisfied".

Based on customer comments, the national customer service group claims that the customer satisfaction ratings at the Forest Hills auto dealership are different than the national ratings. They have compiled data for a random sample of 158 recent Forest Hills customers. Below are the results. Test this claim at the 10% significance level.

a. Select the appropriate null and alternative hypotheses for the chi-square goodness-of-fit test used to test the national customer service group's claim.

H0:

Ha:

b. Compute the value of the chi-square test statistic.

Round intermediate calculations to at least four decimal places. Round your answer to three decimal places.

Chi-square test statistic =

c. Using Excel, compute the p-value for the hypothesis test.

Round your answer to four decimal places. Note: use your unrounded test statistic value to compute the p-value.

p-value =

d. Select the appropriate initial conclusion.

e. Select the appropriate final conclusion.

Rating Extremely satisfied Somewhat satisfied Somewhat dissatisfied Extremely dissatisfied Number of customers 69 49 33 7

Explanation / Answer

Part a)

H0: he customer satisfaction ratings at the Forest Hills dealership are consistent with (equal to) the national ratings.

H1: The customer satisfaction ratings at the Forest Hills dealership are different than the national ratings.

Part b)

X^2 = S (Oi - Ei)^2 / Ei

Oi =observed values

Ei =expected values

158

Expected (%)

100

66.36

47.4

34.76

9.48

Oi - Ei

2.64

1.6

-1.76

-2.48

(Oi - Ei)^2

6.9696

2.56

3.0976

6.1504

(Oi - Ei)^2 / Ei

0.11

0.05

0.09

0.65

0.90

Chi-square test Statistics = 0.90

Part c)

Degrees of freedom =n – 1 = 4 – 1 = 3

=CHIDIST(0.9,3)

p-value = 0.8254

Part d)

Do not reject the null hypothesis

Part e)

Support the national customer service group’s claim.

158