Question

question 8 of 10
suppose a social networking site has roughly 1,000,000 users, and as each member signs up for an account, he or she is assigned a number. which of these would result in the smallest sample size using systematic sampling?
a. surveying every 25,000th number
b. surveying every 2500th number
c. surveying every 25th number
d. surveying every 250th number

Explanation:

Step1: Recall sample size formula

Sample size $n = \frac{N}{k}$, where $N$ is population size, $k$ is sampling interval.

Step2: Calculate sample size for A

$N=1,000,000$, $k=25,000$
$n_A = \frac{1,000,000}{25,000} = 40$

Step3: Calculate sample size for B

$k=2500$
$n_B = \frac{1,000,000}{2500} = 400$

Step4: Calculate sample size for C

$k=25$
$n_C = \frac{1,000,000}{25} = 40,000$

Step5: Calculate sample size for D

$k=250$
$n_D = \frac{1,000,000}{250} = 4,000$

Step6: Compare sample sizes

$40 < 400 < 4,000 < 40,000$

Answer:

A. Surveying every 25,000th number