Question

• For Example 1, Calculate the Sample Size Reqiured for a margin of error of only m=0.5

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 20

σ = 10

n = 64

Confidence level = 99%

Critical Z value = 2.5758

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 20 ± 2.5758*10/sqrt(64)

Confidence interval = 20 ± 3.2198

Lower limit = 20 - 3.2198 = 16.7802

Upper limit = 20 + 3.2198 = 23.2198

Confidence interval = (16.7802, 23.2198)

The sample size formula is given as below:

n = (Z*σ/E)^2

We are given

σ = 10

Confidence level = 99%

Critical Z value = 2.5758

(by using z-table)

Margin of error = E = 0.5

The sample size is given as below:

n = (Z*σ/E)^2

n = (2.5758*10/0.5)^2

n = 2653.898256

Required sample size = 2654