The number of defectives in the samples of 100 observations each are the following: 1,2,1,0,2,3,1,4,2,1.What is the estimate of the population proportion of defectives?
A)0399
B)0098
C)0170
D)0500
E)0813

Question

Quizplus · Accepted Answer

The estimate of the population proportion of defectives can be calculated by taking the average of the sample proportions. 
The sample proportion can be calculated by dividing the number of defectives by the sample size: 
Sample proportion = Number of defectives / Sample size = x/100 
where x is the number of defectives in the sample.

Calculating the sample proportions for each observation: 
1/100 = 0.01
2/100 = 0.02
1/100 = 0.01
0/100 = 0
2/100 = 0.02
3/100 = 0.03
1/100 = 0.01
4/100 = 0.04
2/100 = 0.02
1/100 = 0.01

Taking the average of these sample proportions: 
(0.01+0.02+0.01+0+0.02+0.03+0.01+0.04+0.02+0.01)/10 = 0.017

Therefore, the estimate of the population proportion of defectives is 0.017 or 1.7%. 
The closest answer choice is C) 0.170, which should be divided by 10 to get the correct proportion of 0.017.

The Number of Defectives in the Samples of 100 Observations