From a population of size 600, a simple random sample of size 60 is selected. The sample mean is 400, and the sample standard deviation is 50. An approximate 95% confidence interval for the population total is
A) 350,000 to 450,000
B) 232,800 to 247,200
C) 350 to 400
D) 388 to 412

Question

Quizplus · Accepted Answer

We can use the formula for the confidence interval of a population total:
CI = x̄N ± t(alpha/2,df)*(s/sqrt(n))*sqrt(N-n)
where 
x̄ = sample mean = 400
N = population size = 600
n = sample size = 60
s = sample standard deviation = 50
df = degrees of freedom = n-1 = 59
t(alpha/2,df) = t(0.025,59) = 2.000
Plugging in the values, we get:
CI = 400*600 ± 2.000*(50/sqrt(60))*sqrt(600-60)
CI = 240000 ± 2.000*14.434*sqrt(540)
CI = 240000 ± 29,234.788
CI = (232,765.212, 247,234.788)
The approximate 95% confidence interval for the population total is therefore (232,800 to 247,200), which corresponds to option B.

From a Population of Size 600, a Simple Random Sample