In class midterm: Oct. 16
Homework Assignments (#2)
(Due Tuesday, 09/30)
Note: The problem numbers in parentheses are from the sixth edition.
Chapter 8: # 5, 9, 17, 20, 23, 35, 40, 39 (Note: The wording in the question is not precise.
The “random sample of 1050” referred to in the question was chosen by procedures
developed by the court. The issue here was whether these procedures actually produced a
random sample (as they should have), or merely a sample. Swain’s attorneys – and the
solutions given in the back of our book – used a one-sided test. Suppose you were the
defense lawyer, representing the state of Alabama. How would you argue that a two-
sided test was more appropriate for this situation? Would it have made any substantive
difference to the final evaluation if a two-sided test had been used?)
D. The intended octane rating of the gasoline produced by the company in Problem
B, (HW 1), is 87.
(a) Use the data of problem B to test (at level α = 0.05) whether the
company’s mean octane rating for the day in question was different from
87.
(b) Actually, the company does not claim that its “regular” grade gasoline has
an octane rating of exactly 87. Instead it claims that the octane rating is at
least 87. Perform a test (at level α = 0.05) designed to verify that the
company’s claim is correct.
E. While imprisoned by the Germans in World War II, the English mathematician
John Kerrich tossed his only coin 10,000 times and obtained 5,067 heads. Let p denote
the probability of a head on a single toss. We wish to check whether the data are
consistent with the hypothesis that the coin was fair.
(a) Set up the statistical hypotheses. Why should the alternative be two-sided
even though Kerrich obtained more heads than tails on his 10,000 tosses?
(b) Does your test reject the null hypothesis at α = 0.05?
(c) Find a 95% CI for the proportion of heads for Kerrich’s coin. Does this CI
contain p = ½?
(d) On his first 1,000 flips Kerrich obtained 574 heads. Does this information
alter your conclusions in (b)?
More problems from Chapter 8: #44, 47 (Also, what would be the P-value in each case if
the problem had been to test H
0
: µ = 30 versus H
a
: µ > 30?), 53 (55), 59 (61) (assume
normality), 60 (62), 69 (71), 72 (73), 73 (75), and
1
