Answer to Question #322554 in Statistics and Probability for seung

Question

1.      A study of 40 SHS English teachers established that they spent 12.6 minutes revising a student’s term paper.

a. Find the 90% confidence interval in the mean time for all composition papers when minutes.

b. If the teacher affirmed that she spent an average of 30 minutes revising a term paper, what would be your reaction?

Answer 1

$CI=\mu \plusmn z \frac{\sigma}{\sqrt{n}}$

Z(90%)=1.64

n=40

$\mu=12.6$

$CI=12.6 \plusmn 1.64 \frac{\sigma}{\sqrt{40}}=12.6 \plusmn 0.26 \sigma$

b. $30=12.6+0.26 \sigma$

$\sigma=(30-12.6)/0.26=66.9$

If $\sigma$ smaller then 66.9 min, then 30 min is too long.

If $\sigma$ larger then 66.9, then it is ok.