Q1. A researcher in the West Coast of the U.S. wants to estimate the amount of a newly discovered antibody in human blood. His research funds will only let him obtain blood samples from 41 people, so he decides to construct a two-sided 90% confidence interval thinking it will give him a more precise estimate of the mean antibody level in the population. Another researcher on the East Coast of the United States is researching the same antibody, but has more research funding and can afford to obtain blood samples from 121 people. The East Coast researcher decides to construct a two-sided 99% confidence interval. Which researcher will have the more precise estimate? State your reason for choosing your answer. It may help to imagine that the sample standard deviation will be about the same for both samples.
Q2. Identify a pair of variables for which you would expect to see a strong correlation but not a cause-and-effect relationship. Suggest an explanation for the association.
Q3. Twenty years ago, postal employees worked for the postal service an average of 7.5 years. Recently, a sample of 100 postal employees revealed that the average time these employees had worked for the postal service was (X‾) = 7 years. The population of employee lengths of service has a standard deviation = 5 years. Has decreased from the mean of 7.5 years of 20 years ago? Conduct a hypothesis test (use H0: µ =7.5). Use a .05 significance level. Is this evidence that the average length of employment with the postal service has decreased from twenty years ago?