Basic Statistics Questions Using one sample mean
Here is an example of a statistics question you'll mostly find if you are enrolled in a basic statistics class. Hypothesis tests for this questions uses the one-sample z-test because the population standard deviation has been given.
Prep-Work Problem 11.1
ABC Auditors is investigating client response time when members of its staff follow up with clients requesting additional information. Currently, auditors claim that it takes more than five days for a client to respond with the requested information, To examine this claim, a partner at ABC Auditors asks a random sample of 10 employees to report the number of days it takes clients to respond to their inquiries. The following are the results of this random sample:
Can ABC Auditors conclude at the 5% significance level that it takes more than five days for a client to respond to inquiries assuming that the number of days is normally distributed with a standard deviation of 1.5?
Prep-Work Problem 11.2
Company X is a manufacturer that manufactures expensive computer components. The quality control manager has recently become frustrated with the number of components destroyed during the manufacturing process. He has told the CFO that the average assembly line worker destroys 12 or more components in a single shift. The quality control manager has informed this amount is unacceptable and these assembly line workers should be fired. The CFO is taking this complain seriously but thinks the number of destroyed items is less than what the quality control manager claims. In order to investigate the quality control manager’s claim, the CFO takes a random sample of 15 assembly line employees to see how many components are destroyed by each worker in a single shift. The sample is as follows:
Assuming that the number of destroyed items is normally distributed with a standard deviation of 3, can the CFO infer at the 10% significance level that the average number of destroyed components is less than 12?