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1900 kcal.
(g) The nutritionist would arrive at the same conclusion at α = 0.10.
7. In a survey conducted by Survey USA on July 12, 2010, 827 registered voters in California were asked
“Do you support? Or do you oppose? drilling for oil and natural gas oﬀ the Coast of California? Or
do you not know enough to say?” Below is the distribution of responses based on whether or not the
respondent graduated from college. We might expect that college graduates would be more likely to
have an opinion on this issue than noncollege graduates. Therefore we are interested in ﬁnding out if
the proportion of college graduates who do not have an opinion on the matter, i.e. responded do not
know, is lower than the proportion of noncollege graduates who do not have an opinion on the matter. Response Support
Oppose
Do not know
Total College
Yes
154
180
104
438 Grad
No
132
126
131
389 i. What percent of the college graduates and what percent of the noncollege graduates in this
sample do not know enough to have an opinion on drilling for oil and natural gas oﬀ the Coast of
California?
104
= 0.237
438
131
P (Do not knowN on College Grad) =
= 0.337
389
P (Do not knowCollege Grad) = 4 ii. Which of the below is the appropriate set of hypotheses?
(a) H0 : pcollege grad = pnon college grad
ˆ
ˆ
HA : pcollege grad < pnon college grad
ˆ
ˆ
(b) H0 : pcollege grad = pnon college grad
HA : pcollege grad = pnon college grad
(c) H0 : pcollege grad = pnon college grad
HA : pcollege grad < pnon college grad
(d) H0 : µcollege grad = µnon college grad
HA : µcollege grad < µnon college grad
iii. Calculate the test statistic.
104 + 131
235
=
= 0.284
438 + 389
827
qpooled = 1 − 0.284 = 0.716
ˆ
p1 − p2
ˆ
ˆ
0.237 − 0.337
−0.1
z=
=
=
= −3.18
ppooled qpooled
ˆ
ˆ
p
ˆ
q
ˆ
0.0314
0.284∗0.716
+ 0.284∗0.716
+ pooled 2pooled
438
389
n1
n ppooled =
ˆ iv. Calculate the pvalue.
p − value = P (z < −3.18) = 0.0007
v. What is the conclusion of the hypothesis test? Make sure to interpret your conclusion in context.
Since pvalue < α (0.05), we reject H0 . There is sucient evidence to suggest that the proportion of college graduates who responded do not know is lower than the proportion of noncollege
graduates who responded do not know.
8. A professor believes that students perform better on an introductory statistics exam if they are only
allowed one sheet of notes (“cheat sheet”) compared to an “open book” exam (where they have access
to all notes, textbook, etc.). To test his theory he randomly assigned the 50 students in his class to
two groups: one group took the exam with just a “cheat sheet”, and the other group took the same
exam “open book”. On average students in the “cheat sheet” group scored 6 points higher than the
students in the “open book” group.
(a) Write the hypotheses for testing the professor’s theory.
H0 : µcheat sheet = µopen book
HA : µcheat sheet > µopen book
(b) To test these hypotheses the professor use...
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This document was uploaded on 12/04/2013.
 Winter '13

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