A new process for producing synthetic diamonds can be operated at a profitable l

Question

A new process for producing synthetic diamonds can be operated at a profitable level only if the average weight of the diamonds produced by the process is greater than 0.5 karat. To evaluate the profitability of the process, a sample of six diamonds was generated using this new process, with recorded weights .46, .61, .52, .48, .57, and .54 karat. Do the six measurements present sufficient evidence to indicate that the average weight of the diamonds produced by the new process is in excess of 0.5 karat?

To answer this question, conduct an appropriate test of hypothesis using the five step process outlined in Elementary Statistics: A brief version from Bluman textbook.

Explanation / Answer

Given n=6, xbar= 0.53, s=0.056 (based on the data)

The test hypothesis is
Ho:<=0.5
Ha:>0.5

The test statistic is

t=(xbar -mean)/(s/n)

=(0.54-0.5)/(0.056/sqrt(6))

=1.75

If a=0.05, the critical value is |t(0.05, df=n-1=5)|=2.02 (check student t table)

Since t=1.75 is less than 2.02, we do not reject Ho.

So we can not conclude that the average weight of the diamonds produced by the new process is in excess of 0.5 karat.

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