Question

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Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is...

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.)

Solutions

Expert Solution

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 = Z0.025 = 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


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