Question

An SRS of 2,500 individuals was taken from a city with population 1 million, to estimate the percentage of city residents with a graduate degree. 555 people in the sample had a graduate degree. The proportion of individuals in the city with a graduate degree is estimated as 23%. Say the true percentage of individuals in the city who have a graduate degree is 22%. In this case, the standard error of the sample proportion is closest to:

Answer 1

The standard error of the sample proportion is closest to 1%

Explanation:

Standard error of the sample proportion is given as

σₓ = √[p(1-p)/n]

where

p = sample proportion = estimated to be 23% = 0.23

n = Sample size = 2500

σₓ = √[p(1-p)/n]

σₓ = √[0.23×0.77/2500]

σₓ = 0.0084166502 = 0.00842

σₓ = 0.00842 = 0.842%

Hence, it is easy to see that the standard error of the sample proportion is closest to 1%.

Hope this Helps!!!