Question

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.77.

(c) How large a sample size is necessary if the width of the 95% interval is to be 0.42? (Round your answer up to the nearest whole number.)

(d) What sample size is necessary to estimate true average porosity to within 0.23 with 99% confidence? (Round your answer up to the nearest whole number.)

Answer 1

solution

standard deviation = =0.77

Margin of error = E = width/2=0.42/2=0.21

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05 / 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96 ( Using z table )

sample size = n = [Z_/2* / E] ²

n = ( 1.96*0.77/0.21 )²

n =52

Sample size = n =52

given that,

standard deviation =0.77

Margin of error = E = 0.23

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z_/2 = 2.58 ( Using z table )  

sample size = n = [Z_/2* / E] ²

n = ( 2.58*0.77 / 0.23 )²

n =75

Sample size = n =75