Stat 321 – HW 7

Due Tuesday, March 4

1) Exercise #60 (p. 222), a bit more practice on working with combinations of random variables. Use (and show lots of details) the rules for variance and expected value and remember that linear combinations of independent normal random variables will also follow a normal distribution.

2) Exercise #2 (p. 262)

3) In 1936, Literary Digest magazine conducted the most extensive (to that date) public opinion poll in history. They mailed out questionnaires to over 10 million people whose names and addresses they obtained from telephone books and vehicle registration lists. More than 2.4 million responded, with 57% indicating that they would vote for Republican Alf Landon in the upcoming presidential election.

(a) Identify the population of interest and the sample. Also define the parameter and statistic.

(b) Use equation (7.11, p. 266, the Wald procedure) with these data to calculate and interpret a 99.9% confidence interval for the parameter you described in (a). Is the sample size large enough that this procedure should be valid?

(c) Incumbent Democrat Franklin Roosevelt won the election, carrying 63% of the population vote. Does this agree with the confidence interval you calculated in (b)?

(d) Give two explanations why the Literary Digest prediction was so much in error. In particular, talk about the direction of the bias – why was this sampling method vulnerable to producing an overestimate of the parameter?

(e) Suppose the Literary Digest instead was able to select a random sample of all eligible voters. What sample size would be required for the margin-of-error (i.e., half-width) of a 99% confidence interval to be at most .05, irrespective of ? (Review p. 257)

4) Exercise #33 (p. 277)

You are encouraged to use Minitab but remember to include all relevant output.

Also add (d) Calculate a 95% confidence interval for the degree of polymerization for an individual paper specimen under these conditions. Does the interval suggest that 440 is a probable value for degree of polymerization?

Please also consider but you do not need to submit Exercise #3 (p. 262)