A mining company made some changes to their mining process i

A mining company made some changes to their mining process in an attempt to save fuel. Before the changes were made, it took an average of 20 gallons of diesel fuel to mine 1,000 pounds of copper. Suppose the standard deviation of fuel used per 1,000 pounds of copper mined is 6 gallons. After the changes were made, the company only used an average of 18 gallons of diesel for the next 30,000 pounds of copper mined.

A. What is the probability to get a sample average of 18 gallons or less for 30,000 pounds of copper mined if the changes to the mining process had no effect?

B. Do you think the changes in the mining process actually lowered the fuel used? Explain

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Solution

a)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    18      
u = mean =    20      
n = sample size =    30      
s = standard deviation =    6      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1.825741858      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.825741858   ) =    0.033944577 [ANSWER]

You can type =NORMSDIST(-1.825741858) in Excel to get this.

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b)

Yes, because the probability of this event happening or a more extreme event is less than 0.05. [ANSWER]