Question: A quality control inspector randomly removed a small sample of light bulbs from an assembly line and turned them on, to see how long they would burn. Here are the numbers of hours her experiment produced: 972, 854, 952, 893, 945, 909, 850, 918, 909, 980, 926, 883, 925.

a. The first thing the inspector wants to know is whether she can be 95% certain that the average bulb from the factory burns at least 900 hours, as stated on its package.

i. What is the null hypothesis for her hypothesis test?

ii. What is the significance level of the test?

iii. What is the value of the test statistic she computes?

iv. What value of the test statistic is critical?

v. What numbers could she compare in order to make up her mind?

vi. How could she express her conclusion in language which any literate person could understand?

b. The second thing the inspector is worried about is if there is too much variation among the lifetimes of bulbs. She believes that the factory standard deviation should be no more than 35 hours.

i. What sort of statistical test should settle this question?

ii. Perform the test you selected, and explain to the inspector your basis for saying whether or not she has cause to be worried about the amount of variation.