Question

A call center claims their average call lasts 6 minutes. Let's take a sample of 30 call center agents with a mean of 7.2 minutes and a standard deviation of 1.9 minutes. Can the claim at an alpha of 0.08?

Answer 1

Solution:

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

The null and alternative hypotheses are given as below:

H0: µ = 6 versus Ha: µ ≠ 6

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 6

Xbar = 7.2

S = 1.9

n = 30

df = n – 1 = 29

α = 0.08

Critical value = - 1.8142 and 1.8142

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (7.2 - 6)/[1.9/sqrt(30)]

t = 3.4593

P-value = 0.0017

(by using t-table)

P-value < α = 0.08

So, we reject the null hypothesis

There is not sufficient evidence to conclude that the average call lasts 6 minutes.