Math 143 C/E, Spring 2001
IPS Reading Questions
Chapter 6, Section 1 (pp. 432-445; up to “Beyond the basics”)

1. On p. 435 in the paragraph below Example 6.1, the authors say what it means for the sample mean to be an unbiased estimator of the population mean. How do they put it?

   
   
   
   
   
   

2. Determine the following probabilities for the standard normal distribution:

   1. P(-1.645 < Z < 1.645)
   2. P(-1.960 < Z < 1.960)
   3. P(-2.576 < Z < 2.576)

   How should the values of these probabilities be related to the values of C found in the table on p. 439?

   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

3. The authors indicate that it is unrealistic, in practice, for one to know the value of the population's standard deviation s. For now, however, the problems assigned will provide this information as if it can be known. Assuming you have it, how do you determine the margin of error corresponding to a given level of confidence for the mean of a sample?

   
   
   
   
   
   
   
   
   
   

4. Just what is a 99% confidence interval? Apply your interpretation to the scenario in which a television news organization claims that Candidate A is projected to carry the State of Michigan with 95% confidence 56%±3%.

   
   
   
   
   
   
   
   
   
   
   
   

5. Why do each of the three bulleted items on p. 442 decrease the margin of error?

   
   
   
   
   
   
   
   
   
   
   

6. Read the fine print. On pp. 444-45, you are told just how trustworthy our inference procedure of finding confidence itervals is.