Question

Determine the minimum sample size required when you want to be 90% confident that the sample mean is within one unit of the population mean and σ=10.8 Assume the population is normally distributed.

Find the critical value Tc for the confidence level c=0.80 and sample size n=19.

Answer 1

Solution :

Given that,

standard deviation =s =   =10.8

Margin of error = E = 1

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 *10.8 / 1 )2

n =316

Sample size = n =316

B.

n=19

df=n-1=19-1=18

At 80% confidence level the t is

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20/ 2 = 0.10

t /2,df = t0.10,18 = 1.330 ( using student t table)