1. 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...

1. 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.
2. 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.
3. 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 () = 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?
5. Use the SPSS output to determine if there is sufficient evidence to conclude that Sally bakes a better pie than Pat (i.e., the average rating for Sally at her church is higher than the average rating for Pat at her church). Justify your conclusion.
6. A nutritionist thinks the average person with an income below the poverty level gets less than the recommended daily allowance (RDA) of 800 mg of calcium. To test her conjecture, she obtains the daily intakes of calcium for a random sample of 45 people with incomes below the poverty level. The mean of the sample is 737.3 mg with sample standard deviation of 262.2 mg. Is there sufficient evidence at the alpha =0.05 level to support the researcher's claim?