Question

The chair of the operations management department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are in control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results: Instructor Number of Failures Prof. A 13 Prof. B 0 Prof. C 11 Prof. D 16 What is the estimate of the standard deviation of the sampling distribution for an instructor's sample proportion of failures?

Answer 1

0.03

Explanation:

Given the following :

Instructor __no of failure __prop (failure /100)

A ________ 13__________0.13

B ________0___________0

C________11___________0.11

D________16__________0.16

Prof. B adds no proportion to the data and hence excluded in the estimation.

Mean(m) = 0.13 + 0.11 + 0.16) / 3

= 0.4 / 3

= 0.1333

Standard deviation :

Σ(X - m)² / N - 1

Σ(0.13 - 0.1333)² + (0.11 × 0.1333)² + ( 0.16 - 0.1333)² = 0.0012668689

= 0.0012668689 / 2

= 0.00063343445

√0.00063343445

= 0.0251681

= 0.03 To 2 decimal places