Question

1. A simple random sample of 48 calls is monitored at an in-bound call center and the average length of the calls is 8 minutes. The population standard deviation σ is unknown. Instead the sample standard deviation s is also calculated from the sample and is found to be 4 minutes.

    (9 marks)

1. Construct a 99% confidence interval (using the t-distribution) for the average length of inbound calls.

2. What is the margin of error at the 95% confidence level?

3. Do we need to make any assumption on the distribution of the length of in-bound calls at this call center? Why or why not?

Answer 1

a. The 99% confidence interval (using the t-distribution) for the average length of inbound calls is ,

; from excel "TINV(0.01,47)"

b. The margin of error is ,

c) Now , we need to make the following assumption on the distribution of the length of in-bound calls at this call center.

i) The data is simple random sampling.

ii) The observations should be independent.

iii) The sampling distribution is approximately normal.

While constructing the confidence interval , the assumptions and conditions of the central limit theorem must be satisfy.