Question

A large accounting firm tsts a new software with 10 randomly selected employees. It measures the time that the employees take in finishing a particular type of task with the existing software in use and then measures the time that they take with the new software. They compute the difference d=(new-old) for each of these 10 employees to be able to estimate ud. In the comparison, they find that the mean of the differences is -67 minutes and standard deviation 12 minutes. Construct a 95 % confidence interval for the mean of such differences for the entire population of their employees. Assume a normal population.

Answer 1

Since the same employees are use for before and after treatment, it is a paired t-test or will use paired t-distribution.

Let the difference be denoted by 'D'

We will use t-distribution for confidence interval

95% confidence interval for mean difference is given by

The critical value is found using t-dist tables

Critical Value =

=      So

= 2.262

Substituting other values