Question

Determine the sample size n needed to construct a 95​% confidence interval to estimate the population mean for the following margins of error when sigma equals 67.

​a) 25 ​b) 40 ​c) 50

Answer 1

:

Solution

standard deviation =s =   =67

Margin of error = E = 25

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z/2* / E] 2

n = ( 1.96* 67 / 25)2

n =28

Sample size = n =28

b.

standard deviation =s =   =67

Margin of error = E = 40

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z/2* / E] 2

n = ( 1.96* 67 / 40)2

n =11

Sample size = n =11

c.

standard deviation =s =   =67

Margin of error = E = 50

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z/2* / E] 2

n = ( 1.96* 67 / 50)2

n =7

Sample size = n =7