Question

A customer service phone line claims that the wait times before a call is answered by a service representative is less than 3.3 minutes. In a random sample of 62 calls, the average wait time before a representative answers is "3.24" minutes. The population standard deviation is assumed to be 0.40 minutes. Can the claim be supported at α=0.08?

Answer 1

Explanation:

Let x be the wait times before a call is answered in phone calls.

The claim is x bar <3.3 minutes

Sample size n =62

Sample mean - x bar = 3.24 minutes

Population std dev =
`\sigma = 0.40 minutes\\`

Since population std dev is known and also sample size is sufficiently large, we can use Z test.

`H_0: x bar = 3.3\\H_a: x bar <3.3`

(one tailed test)

Mean difference = 3.24-3.3 = -0.06 min

Std error of sample =
`(\sigma)/(√(n) ) =(0.40)/(√(62) ) \\=0.0508`

Z = tset statistic =
`(-006)/(0.0508) \\\\=-1.18`

p value = 0.119

Since p value > alpha, we accept null hypothesis.

There is no evidence to support the claim at alpha = 0.08