Question

Suppose that a population parameter is 0.5 and many large samples are taken from the population. If the sample proportions are normally distributed, with 99.7% of the sample proportions falling between 0.434 and 0.566, what is the standard deviation of the sample proportions?

A. 0.025
B. 0.015
C. 0.011
D. 0.022

Answer 1

The margin of error of the 99.7% confidence interval is 
     $ME=0.566-0.5=0.5-0.434=0.066$

This computed margin or error is actually 3 standard deviations from the mean according to the empirical rule. The empirical rule states that 3 standard deviations away from the mean constitute the 99.7%.

Therefore, the value 0.066 is 3 times the standard deviation. The standard deviation, SE, is 
     $SE=0.066\div 3=0.022$

The standard deviation is 0.022.