Case Study 13.1: National Oil Company – Guidance and Further Instructions
National Oil Company—Part 2
Chad Williams sat back in his airline seat to enjoy the hour-long flight between Los Angeles and Oakland, California. (See Case 6.3.) The hour would give him time to reflect on his upcoming trip to Australia and the work he had been doing the past week in Los Angeles.
Chad is one man on a six-person crew employed by National Oil Company to literally walk the Earth searching for oil. His college degrees in geology and petroleum engineering landed him the job with National, but he never dreamed he would be doing the exciting work he now does. Chad and his crew spend several months in special locations around the world using highly sensitive electronic equipment for oil exploration.
The upcoming trip to Australia is one that Chad has been looking forward to since it was announced that his crew would be going there to search the Outback for oil. In preparation for the trip, the crew has been in Los Angeles at National’s engineering research facility working on some new equipment that will be used in Australia.
Chad’s thoughts centered on the problem he was having with a particular component part on the new equipment. The specifications called for 200 of the components, with each having a diameter of between 0.15 and 0.18 inch. The only available supplier of the component manufactures the components in New Jersey to specifications calling for normally distributed output, with a mean of 0.16 inch and a standard deviation of 0.02 inch.
Chad faces two problems. First, he is unsure that the supplier actually does produce parts with a mean of 0.16 inch and a standard deviation of 0.02 inch according to a normal distribution. Second, if the parts are made to specifications, he needs to determine how many components to purchase so that he receives enough acceptable components to make two oil exploration devices.
The supplier has sent Chad the following data for 330 randomly selected components. Chad believes that the supplier is honest and that he can rely on the data.
Chad needs to have a report ready for Monday indicating whether he believes the supplier delivers at its stated specifications and, if so, how many of the components National should order to have enough acceptable components to outfit two oil exploration devices.
Required Tasks:
1. State the problem faced by Chad Williams.
2. Briefly summarize the data (include an explanation of the results of descriptive statistics of the data, variable(s) included, how the data was collected, and any pertinent information about the data available in the case study)
3. Identify and discuss the statistical test Chad can use to determine whether the supplier’s claim is true.
4. State and justify the null and alternative hypotheses for the test to determine whether the supplier’s claim is true.
5. Assuming that the supplier produces output whose diameter is normally distributed with a mean of 0.16 inch and a standard deviation of 0.02 inch, determine the expected frequencies that Chad would expect to see in a sample of 330 components. Explain the procedure for making these calculations.
6. Based on the observed and expected frequencies, explain how to calculate the appropriate test statistic.
7. Explain how the critical value is obtained for the test statistic. What is the critical value for the test statistic. Select and justify your reasoning of an alpha value.
8. The results of all necessary calculations have been provided below. Students are urged to try to reproduce this results on their own in order to develop additional insight into the calculations.
9. State a conclusion. Do the sample data support the supplier’s claim with respect to the specifications of the component parts?
Diameter (inches) Observed Probability Expected (O-E)2/E
Under 0.14 5 0.15865526 52.35623572 42.83373
0.14 and under 0.15 70 0.149882273 49.46115005 8.528802
0.15 and under 0.16 90 0.191462467 63.18261416 11.38244
0.16 and under 0.17 105 0.191462468 63.1826143 27.67682
0.17 and under 0.18 50 0.149882273 49.46115005 0.00587
Over 0.18 10 0.15865526 52.35623572 34.26623
Total 330 1.00000 330 124.6939
10. Note: The report is required to explain the conclusion that can be drawn from the appropriate statistical test and to make practical recommendations based on the results of the statistical analyses.
