Assume that the helium porosity of coal samples taken from any particular seam is Normally distributed with true standard deviation 0.75.a. Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85.
b. Compute a 98% CI for true average porosity of another seam based on 16 specimens with a sample average porosity of 4.56.
c. How large a sample size is necessary if the width of the 95% interval is to be .40

a)    

b)    

c)

Step-by-step explanation:

Part a

The confidence interval for the mean is given by the following formula:

  (1)

The Confidence is 0.98 or 98%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that

Now we have everything in order to replace into formula (1):

Part b

Part c  

The margin of error is given by this formula:

   (a)

And on this case we have that ME =0.4/2 =0.2  we are interested in order to find the value of n, if we solve n from equation (a) we got:

  (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got , replacing into formula (b) we got: