**Question 2**

**Complete both parts (a) and (b).**

**(a).** A call center claims that the average time it takes to answer a call is 2 minutes. Following several complaints, a regulatory agency decided to test the company’s claim. The time taken (in minutes) to answer 100 customer calls on a particular day was recorded. A selection of summary statistics and a boxplot are shown below:

n Minimum Maximum Mean Std.Deviation

1 100 1.85 4.09 3.05 0.46

**(i)** Provide a 95% confidence interval estimate of the population mean, μ, and an interpretation- tion of the result with reference to this application.

**(ii)** Using the confidence interval from part (i), do you agree or disagree with the claim that the average time to answer calls for the population of customers of interest is 2 minutes?

**(iii)** List one concern you might have relating to the sample that this analysis is based on.

**(b).** A random sample of 25 employees from the call centre were asked to record their level of job dissatisfaction on a scale from 0 to 100 where high values represent higher levels of dissatisfaction. A summary of their results is as follows:

n Minimum Maximum Mean Std.Deviation

1 25 67 74.8 70.38 2.12

**(i)** The call center believes the average job dissatisfaction amongst all its employees is 60. Is there evidence from this sample that the population average job satisfaction is greater than 60, i.e. test the hypotheses H0: μ = 60 versus Ha: μ > 60? Carry out the test at the significance level α = 0.05. Include the calculation of the test statistic, the rejection region for the test statistic, and a conclusion.

**(ii)** Detail any assumptions underlying the hypothesis test carried out in part (i). Does the distribution of the sample of job dissatisfaction scores displayed in the above boxplot provide any concerns over the validity of these assumptions? Give a reason for your answer.

**(iii)** Calculate and interpret a 95% confidence interval for the population mean dissatisfaction score and interpret the result with reference to this application.