A new process for producing synthetic diamonds can be operat

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? Please show all work and do not simply use one of the previous answers.Thanks

Solution

Profitable only if mu >0.5 karat

Sample size = 6

Sample data = .46, .61, .52, .48, .57, and .54

Mean = 0.53

Mean difference = 0.03

std dev 0.05099

Std error = 0.226

t statistic = 0.133

df = 5

alpha = 0.05 (say)

H0: mu = 0.5

Ha: ,mu>0.5

One tailed test

P-Value is .44969.

The result is not significant at p < .05.

As p >0.05 we accept null hypothesis that mu =0.5 karat

the six measurements does not present sufficient evidence to indicate that the average weight of the diamonds produced by the new process is in excess of 0.5 karat