Question

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.79. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 22 specimens from the seam was 4.85. (Round your answers to two decimal places.)

Answer 1

Interval=4.85±0.33

Interval (5.18,4.52)

Explanation:

Consider the formula for the interval:

interval=
`X`±
`(Z*S)/(√(n) )`

Where:

X is the mean value

S is the standard deviation

n is the sample size

Z is the distribution

Alpha=1-0.95=0.05

`Z_(alpha/2)=Z_(0.05/2) =Z_(0.025)`=1.96 (From Standard Z-Distribution Table)

Now use the above formula

interval=
`4.85`±
`(1.96*0.79)/(√(22) )`

Interval=4.85±0.33

Interval (5.18,4.52)