Question: American Oil Company Chad Williams sat back in his airline seat to enjoy the hour-long flight between Los Angeles and Oakland, California. 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-man crew employed by the American Oil Company to literally walk the earth searching for oil. His college degrees in geology and petroleum engineering landed him the job with American, 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 American'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 inches and a standard deviation of 0.02 inches.
Chad faces two problems. First, he is unsure that the supplier actually does produce parts with means of 0.16 inches and standard deviations of 0.02 inches according to a normal distribution. Second, if the parts are made to specifications, he needs to determine how many components to purchase if enough acceptable components are to be received 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 American should order to have enough acceptable components to outfit two oil exploration devices.
Required Tasks: 1. State the problems faced by Chad Williams.
2. Identify the statistical test Chad Williams can use to determine whether the supplier's claim is true.
3. State the null and alternative hypotheses for the test to determine whether the supplier's claim is true.
4. Assuming that the supplier produces output whose diameter is normally distributed with a mean of 0.16 inches and a standard deviation of 0.02 inches, determine the expected frequencies that Chad would expect to see in a sample of 330 components.
5. Based on the observed and expected frequencies, calculate the appropriate test statistic.
6. Calculate the critical value of the test statistic. Select an alpha value.
7. State a conclusion. Is the supplier's claim with respect to specifications of the component parts supported by the sample data?
8. Provide a short report that summarizes your analysis and conclusion.