A simple random sample of 100 bags of tortilla chips produced at Plant A is selected every hour for quality control.In the current sample,18 bags had more chips (measured in weight)than the labeled quantity.This sample information is being compared to data collected at Plant B.In the current sample of 100 bags of chips from Plant B,12 bags had more chips than the labeled quantity.Let represent the plus four estimate of the difference in the two proportions.What is the value of the standard error of ?
A)0.0384
B)0.0503
C)0.0508
D)0.0604

Question

A simple random sample of 100 bags of tortilla chips produced at Plant A is selected every hour for quality control.In the current sample,18 bags had more chips (measured in weight)than the labeled quantity.This sample information is being compared to data collected at Plant B.In the current sample of 100 bags of chips from Plant B,12 bags had more chips than the labeled quantity.Let  represent the plus four estimate of the difference in the two proportions.What is the value of the standard error of  ?
A)0.0384 
B)0.0503 
C)0.0508 
D)0.0604

Quizplus · Accepted Answer

We can use the formula for standard error of the difference between two proportions:

SE = sqrt [(p1 * (1 - p1))/n1 + (p2 * (1 - p2))/n2]

where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

In this case,

p1 = 18/100 = 0.18
n1 = 100
p2 = 12/100 = 0.12
n2 = 100

Plugging in the values, we get:

SE = sqrt [(0.18 * 0.82)/100 + (0.12 * 0.88)/100] 
   = sqrt (0.001296 + 0.001056)
   = sqrt (0.002352) 
   = 0.0508

Therefore, the value of the standard error is 0.0508.

The best choice is C.

A Simple Random Sample of 100 Bags of Tortilla Chips