Question

An economist is interested in studying the incomes of consumers in a particular country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100

Answer 1

Answer:

The sample size concentrates on managing the method of selecting a certain number of observations in order to incorporate them into a statistical sample.

Explanation:

At 95% confidence level, z = 1.960

Given that:

E = 50

Standard Deviation (sd) = $1,000

$E = z * sd / sqrt{n}$

$50 = 1.960 * 1000 / sqrt{n}$

$n = (1.960 * 1000 / 50)^{2}$

$n = 1.960 * 20)^{2}$

$n = 1.960 * 20)^{2}$

n = 1536.64