Question

A 95% Z-interval was calculated to be (76.08, 83.92) and σ = 16.
Use this information to find the point estimate used... Margin of error used? Sample size used?

Answer 1

Solution:

We are given

Confidence level = 95%

So, critical Z value = 1.96

(by using z-table)

σ = 16

E = Margin of error = Z*σ/sqrt(n)

We are given

Xbar – E = 76.08

Xbar + E = 83.92

So, by adding these two equations, we get

2Xbar = 160

Xbar = 160/2 = 80

Point estimate = Sample mean = Xbar = 80

Xbar + E = 83.92

80 + E = 83.92

E = 83.92 – 80

E = 3.92

Z*σ/sqrt(n) = 3.92

1.96*16/sqrt(n) = 3.92

31.36/sqrt(n) = 3.92

Sqrt(n) = 31.36/3.92 = 8

n = 8^2 = 64

Required sample size = 64