Question

Consider that you are fabricating reaction vessels that are to be rated for 500 psi. The vessels obviously have a range of bursting pressures...but you certainly can't measure all of the bursting pressures, because then you would have nothing to sell. Suppose you measure the bursting pressure of a sample of the vessels. You ask the question: is there any evidence that the average bursting pressure of the population would be less than 500 psi? You don't want to sell a vessel that is going to burst...

Here are the data that you have obtained:

Vessel ID	Bursting pressure (psi)
1	520
2	535
3	485
4	525
5	505
6	515
7	555
8	520
9	525
10	545

Using these data and the information you have learned in Chapters 8 and 9, please answer the following questions:

1. Is there any evidence that the average bursting pressure of the population would be less than 500 psi? Explain.
2. Would you feel comfortable selling the remaining reaction vessels and marking them with a rating of 500 psi? Explain.
3. Would you feel comfortable using one of the remaining reaction vessels for a reaction for which the pressure could theoretically reach 500 psi? What about for a reaction that would reach 475 psi? 450 psi? Explain your reasoning for each pressure level.

Answer 1

Bursting pressure (psi)
Mean	523
Standard Error	6.244998
Median	522.5
Mode	520
Standard Deviation	19.74842
Sample Variance	390
Kurtosis	0.680082
Skewness	-0.29051
Range	70
Minimum	485
Maximum	555
Sum	5230
Count	10

Is there any evidence that the average bursting pressure of the population would be less than 500 psi? Explain.

Would you feel comfortable selling the remaining reaction vessels and marking them with a rating of 500 psi? Explain.

Yes, the confidence interval is above the 500 psi limit, we will be comfortable selling the remaining reaction vessels and marking them with a rating of 500 psi.

Would you feel comfortable using one of the remaining reaction vessels for a reaction for which the pressure could theoretically reach 500 psi? What about for a reaction that would reach 475 psi? 450 psi? Explain your reasoning for each pressure level.

Yes, all the pressures are lower than 500 psi, we would feel comfortable using one of the remaining reaction vessels for a reaction for which the pressure could theoretically reach 500, 475 or 450 psi