4) An economist is interest 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

Population standard deviation б =1000

95% confidence interval width should not be more than $100.

Hence, (x+E) - (x-E) ≤ 100

2E ≤ 100

E ≤ 100/2

E ≤ 50

Level of significance is ∝ = 0.05 . Using the normal area table values at 0.05, the critical value is Z(∝/2) = 1.96

Computation of the sample size required.

n = [ (Z(∝/2) * б) / E]^2

n = [1.96  * 1000 / 50]^2

n = 39.2^2

n = 1536.64

n = 1537

Hence, the economist needed a sample size of 1537 for a 95% confidence interval if the width of the interval should not be more than $100.

or

really your just stupid if you don't know this

step-by-step explanation: