Question

One of the major measures of the quality of service provided by any organization is the speed with which it responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from 2 installation crews to an installation supervisor, a measurer, and 15 installation crews. The store had the business objective of improving its response to complaints. The variable of interest was defined as the number of days between when the complaint was made and when it was resolved. Data were collected from 50 complaints that were made in the past year with sample mean 43.04 and sample standard deviation 41.9261.

a. The installation supervisor claims that the mean number of days between the receipt of a complaint and the resolution of the complaint is 19 days. At the 0.01 level of significance, is there evidence that the claim is not true (i.e., the mean number of days is different from 19)?

b. What assumption about the population distribution is needed in order to conduct the t test in (a)?

Answer 1

Part a

Here, we have to use one sample t test for the population mean.

Null hypothesis: H₀: the mean number of days between the receipt of a complaint and the resolution of the complaint is 19 days.

Alternative hypothesis: H_a: the mean number of days between the receipt of a complaint and the resolution of the complaint is different from19 days.

H₀: µ = 19 versus H_a: µ ≠ 19

We are given

Level of significance = α = 0.01

Xbar = 43.04

S = 41.9261

n = 50

df = n – 1 = 49

Critical t value = -2.6800 and 2.6800

(by using t-table)

Test statistic formula is given as below:

t = (Xbar - µ) / [S/sqrt(n)]

t = (43.04 – 19) / [41.9261 / sqrt(50)]

t = 4.0545

P-value = 0.0002

(by using t-table)

P-value < α = 0.01

So, we reject the null hypothesis

At the 0.01 level of significance, there is evidence that the claim is not true.

There is insufficient evidence to conclude that the mean number of days between the receipt of a complaint and the resolution of the complaint is 19 days.

Part b

For this test, we assume that the population distribution is normally distributed. The assumption of normality is required for above one sample t test for the population mean.