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 105.6 minutes, with a standard deviation of 71.7 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)

Answer 1

Given that,

=  105.6

s =71.7

n = 13

Degrees of freedom = df = n - 1 = 13- 1 =12

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

= 0.1

t ,df = t0.1,12 =1.356    ( using student t table)

Margin of error = E = t,df * (s /n)

=1.356 * ( 71.7/ 13) = 26.97

The 90% confidence interval estimate of the population mean is,

- E

105.6- 26.97

78.6

lower bound=78.6