Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100, with a sample size of (i) 484 and (ii) 1764. what is the effect of the sample size?

i) M.E = 1.96×100/√484

M.E = 8.91

ii) M.E = 1.96×100/√1764

M.E = 4.67

Therefore, the margin of error decreases as the sample size increases.

Step-by-step explanation:

Margin of error in statistics can be defined as a small amount that is allowed for in case of miscalculation or change of circumstances.

For a statistical data margin of error can be expressed as;

M.E = zr/√n

Given that;

Standard deviation r = 100

Confidence interval = 95%

sample size n1 = 484, n2 = 1764

Z(at 95% confidence interval) = 1.96

i) M.E = 1.96×100/√484

M.E = 8.91

ii) M.E = 1.96×100/√1764

M.E = 4.67

Therefore, the margin of error decreases as the sample size increases.