Question

A random sample of 13 students were asked how long it took them to complete a certain exam. The mean length of time was 117.6 minutes, with a standard deviation of 69.2 minutes. Find the lower bound of the 90% confidence interval for the true mean length of time it would take for all students to complete the exam. Round to one decimal place (for example: 108.1). Write only a number as your answer. Do not write any units.

Answer 1

Here n= 13 , = 117.6, s = 69.2

The confidence level = c = 0.90, so

Sample size is less than 30, so we find t interval. Hence df = n-1 = 13-1 = 12

The lower bound of 90% confidence interval is given by,

- E

Where,

tc = ----------( using excel formula " =t.inv.2t(0.10,12)" )

Hence,

= 34.20

Hence the lower bound is,

117.6 - 34.20 = 83.4