Question

A study of 40 English composition professors showed that they spent, on average, 13 minutes correcting a student's term paper. The standard deviation was 2 min. a. Find and the 90% confidence interval for the mean grading time of all composition papers. < μ < b. intrepret the meaning of the confidence interval you found in part a. b. Does the confidence interval, at 90% confidence level, provide sufficient evidence that the mean time English composition professors spend on grading term papers exceeds 11 minutes? Write an appropriate inequality to justify your answer.

Answer 1

Answer:

a)

90% confidence interval for the mean grading time of all composition papers.

(12.47981 , 13.52019)

b)

Appropriate inequality

The interval is  ( 12.47981 < μ < 13.52019)

Step-by-step explanation:

Explanation:-

a)

Given sample size 'n' = 40

Mean of the sample = 13 minutes

standard deviation = 2 min

level of significance = 0.10 or 90%

90% confidence interval for the mean grading time of all composition papers.

$( x^{-} - Z_{0.1} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.10} \frac{S.D}{\sqrt{n} } )$

 $( 13 - 1.645 \frac{2}{\sqrt{40} } , 13 +1.645 \frac{2}{\sqrt{40} } )$

( 13 - 0.52019 , 13 + 0.52019)

(12.47981 , 13.52019)

b)

The interval is  ( 12.47981 < μ < 13.52019)