Question

1. You work for company that mines and processes vermiculite, which is a type of swelling clay. When vermiculite is heated to high temperatures, water in the vermiculite expands and is released as steam. This release pushes the vermiculite layers apart, leaving a light, slightly compressible product that is often sold for packing insulation or a soil additive.

Through past experience, you have found that the vermiculite must have a water content of 6.8 to expand optimally. You are in charge of exploration, and you have recently found a new vermiculite deposit. You have acquired samples from nine boreholes within the new deposit, and the water content of each sample is given below. You need to decide whether it is economically reasonable to develop this deposit. If your criteria is that there needs to be at least a 10% chance that the new deposit will have a mean water content of 6.8, should you develop this deposit? Explain your answer using statistical justification.

Water content values: 6.3       5.5       5.7      6.8      7.6      5.4      6.9      6.8      5.7

Answer 1

There are multiple ways to address this problem .

A. You can use basic statistics and calculate 90th percentile value , which indicates value which is greater than 90% of samples, i.e 10% of value will be greater than this. You can use excel/minitab to calculate the same .

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
Water content 9 0 6.300 0.256 0.768 5.400 5.600 6.300 6.850

Variable Maximum
Water content 7.60

this indicates 75th percintile Q3 =6.850 , Hence there is 25% chance that water content will be more than 6.85.

90th percentile value is 7.04. Hence this water deposit can be developed

B Alternatively assuming normal distribution , you can calculate Z score for 6.8 (x-mean)/sigma

Z value is (6.8-6.3)/0.768 = 0.651 which incates a cumulative Prob of 0.74 , Hence there is 26% chance that water content will be more than 6.8.