To try to understand the reason for returned goods the manag

To try to understand the reason for returned goods, the manager of a store examines the records on 40 products that were returned in the last year. Reasons were coded by 1 for “defective,” 2 for “unsatisfactory,” and 0 for all other reasons, with the results shown in the table. 0000200000200000000000010000202000000200 Give a point estimate of the proportion of all returns that are because of something wrong with the product, that is, either defective or performed unsatisfactorily. Assuming that the sample is sufficiently large, construct an 80% confidence interval for the proportion of all returns that are because of something wrong with the product.

Solution

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
We have 5 Unsatisfactory results + 1 Defect, i.e (x)=6
Sample Size(n)=40
Sample proportion = x/n =0.15
Confidence Interval = [ 0.15 ±Z a/2 ( Sqrt ( 0.15*0.85) /40)]
= [ 0.15 - 1.28* Sqrt(0.0032) , 0.15 + 1.28* Sqrt(0.0032) ]
= [ 0.0777,0.2223]