Exercise 10.6 The proportion of adults living in a small town who are college graduates is estimated to be p = 0.6. To test this hypothesis, a random sample of 15 adults is selected. If the number of college graduates in the sample is anywhere from 6 to 12, we shall not reject the null hypothesis that p = 0.6; otherwise, we shall conclude that p = 0.6. (a) Evaluate α assuming that p = 0.6. Use the bino- mial distribution. (b) Evaluate β for the alternatives p = 0.5 and p = 0.7. (c) Is this a good test procedure? Exercise 10.7 Repeat Exercise 10.6 but assume that 200 adults are selected and the fail-to-reject region is defined to be 110 ≤ x ≤ 130, where x is the number of college graduates in our sample. Use the normal approxima- tion. ANSWER EXERCISE 10.7 ONLY
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Exercise 10.6 The proportion of adults living in a small town
who are college graduates is estimated to be p = 0.6.
To test this hypothesis, a random sample of 15 adults
is selected. If the number of college graduates in the
sample is anywhere from 6 to 12, we shall not reject
the null hypothesis that p = 0.6; otherwise, we shall
conclude that p
= 0.6.
(a) Evaluate α assuming that p = 0.6. Use the bino-
mial distribution.
(b) Evaluate β for the alternatives p = 0.5 and p = 0.7.
(c) Is this a good test procedure?
Exercise 10.7 Repeat Exercise 10.6 but assume that 200 adults
are selected and the fail-to-reject region is defined to
be 110 ≤ x ≤ 130, where x is the number of college
graduates in our sample. Use the normal approxima-
tion.
ANSWER EXERCISE 10.7 ONLY
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