Question

Determine the sample size n needed to construct a 90​% confidence interval to estimate the population mean when sigma equals 67 and the margin of error equals 10.

n=???????

Answer 1

Solution :

Given that,

standard deviation =   =67

Margin of error = E = 10

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table ( see the 0.05 value in standard normal (z) table corresponding z value is 1.645 )  

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

n = ( 1.645 * 67 / 10 )2

n =121.47

Sample size = n =122