The proportion of supermarket customers who do not buy store-brand products is to be estimated. Which of the following scenarios would lead to a sampling distribution of the sample proportion with the lowest variability?

a Sample 100 customers from the roughly 2000 customers who shop at one store location.

b Sample 100 customers from the roughly 20,000 customers who shop at the stores citywide.

c Sample 200 customers from the roughly 2000 customers who shop at one store location.

d Sample 300 customers from the roughly 20,000 customers who shop at the stores citywide.

Option C

Step-by-step explanation:

We have to minimize the standard error of the proportion.

We have a finite population (one for the customers who shop at one store location and other bigger that is for the customers who shop at the stores citywide).

The standard error for a finite population can be written as:

For each population, the higher the sample size, the less variablity will have in the estimation of the proportion. So, we are left with option C and D.

We can calculate the standard error for each posibility and compare:

c)  Sample n=200 customers from the roughly N=2000 customers who shop at one store location.

d) Sample 300 customers from the roughly 20,000 customers who shop at the stores citywide.

It will give less variability the Option C.

It is assumed that sampling only one store is representative of the parameter of the population of study.

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)