Math& 146 8 am Exam: Inferential Theory Spring 2014
One page of Notes, Closed Book, Calculator OK
Name ___________________________ Points _______/71
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Attendance ___/5 Total ____/76
On this exam, to get full credit for conclusions from the hypothesis test, your choice must be
both correct and consistent with a valid p-value.
1. Because big money donations to politicians lead to favoritism for the wealthy, there is an
ongoing debate about how to finance campaigns fairly, with the normal suggestion being to
make all donations public. Yale law professors have proposed a different strategy. They are
proposing that all donations be secret – in fact, even the politician won’t know who made
donations so that they won’t know who they should do favors for. This would be done by having
donations sent to a clearinghouse which then disperses the money over a period of weeks to the
designated candidates. This is a very different idea that might take a while for people to accept.
Suppose researchers hypothesized that less than 30% of current or past elected officials who hear
this idea will like it. The hypotheses they will test are H0: p = 0.30, H1: p < 0.30. Six
politicians are randomly selected.
(2 pts) 1a. What is the probability that the third randomly selected politician likes the idea?
1a_________
(2 pts) 1b. What is the probability that the fifth randomly selected politician doesn’t like the
idea?
1b_________
(2 pts) 1c. Of the six politicians that were randomly selected, what is the probability that the
second and third liked the idea but the others didn’t? That is, what is P(FSSFFF)?
1c_________
(2 pts) 1d. How many different combinations are there of two successes and four failures?
1d________
(2 pts) 1e. What is the probability that 2 out of 6 randomly selected politicians will like the
idea?
1e_________
http://www.vox.com/2014/5/9/5687204/this-proposal-to-fix-money-in-politics-is-so-crazy-itjust-might-work
http://www.fastcoexist.com/3029110/5-simple-office-policies-that-make-danish-workers-waymore-happy-than-americans
Math& 146 8 am Exam: Inferential Theory Spring 2014
One page of Notes, Closed Book, Calculator OK
Page 2 of 4
(4 pts) 1f. Complete the table below and draw the stick graph to show the binomial distribution
for the possible number (0,1,2,3,4,5,6) of 6 politicians that will support the idea, based on the
hypotheses above.
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0
X=x
P(X=x)
0
1
2
3
4
5
6
(2 pts) 1g. What is the expected value (mean) of this distribution?
1g______________
(2 pts) 1h. What is the standard deviation of this distribution?
1h______________
2.
The public may also not like this plan for not disclosing the source of donations very
well. Test the hypothesis that less than 30% of the public will support this idea. A sample of
560 voters resulted in 157 supporting this idea.
Test the hypotheses (H0: p = 0.30 H1: p < 0.30) using three different methods and a
level of significance of 0.05.
2a. Binomial Distribution: Use the binomial distribution to calculate the exact p-value based on
the data (157 out of 560).
__________________________
(2 pts) Calculator input
___________________
(2 pts) p-value
(3 Cpts) At the 5% level of significance, the proportion of people who think climate change is a
problem _________significantly less than 67% (p = __________, n = ___________)
http://www.vox.com/2014/5/9/5687204/this-proposal-to-fix-money-in-politics-is-so-crazy-itjust-might-work
http://www.fastcoexist.com/3029110/5-simple-office-policies-that-make-danish-workers-waymore-happy-than-americans
Math& 146 8 am Exam: Inferential Theory Spring 2014
One page of Notes, Closed Book, Calculator OK
Page 3 of 4
2b. Normal Approximation: Use the normal approximation to the binomial distribution to
calculate the approximate p-value based on the data (157 out of 560). Provide the requested
information. The mean of the distribution is 168. The standard deviation is 10.84.
_____________
(2 pts)Formula
(3 Cpts)
______________
(2 pts)Substitution
_____________
(2 pts) z value
Which hypothesis is supported by the data?
______________
(2 pts) p-value
Choose 1:
H0
H1
2c. Sampling Distribution for Sample Proportions: Find the p-value using sample proportions
for the data (157 out of 560). Provide the requested information.
(2 pts) Sample proportion ____________________
____________
(2 pts)Formula
_______________
(2 pts)Substitution
_____________
(2 pts) z value
______________
(2 pts) p-value
(3 Cpts) At the 5% level of significance, the proportion of the public who support this idea
_________significantly less than 30% (z= _________ p = __________, n = ___________)
(3 Cpts) Based on the results of the sampling distribution method, does it appear that public
support of this idea is less than 30%?
Choose 1: Yes No
http://www.vox.com/2014/5/9/5687204/this-proposal-to-fix-money-in-politics-is-so-crazy-itjust-might-work
http://www.fastcoexist.com/3029110/5-simple-office-policies-that-make-danish-workers-waymore-happy-than-americans
Math& 146 8 am Exam: Inferential Theory Spring 2014
One page of Notes, Closed Book, Calculator OK
Page 4 of 4
3. Apparently, people living in Denmark are much happier with their work than Americans.
One of the reasons may be the number of hours they spend at work. In Denmark, the average
number of hours at work each year is 1540, with a standard deviation of 150 hours. A sample of
25 Americans will be used to test the hypothesis that Americans work significantly more than the
Danes.
H0: μ = 1540 H1: μ > 1540. Use α = 0.05.
(2 pts) 3a. What is the mean of the sampling distribution of sample means? 3a  x ________
(2 pts) 3b. What is the standard deviation of the sampling distribution of sample means?
3b  x _________
(4 pts) 3c. Draw and label a normal distribution showing the mean and first three standard
deviations on each side of the mean for a sample of 25 Americans.
3d, If the mean number of hours worked in a year for 25 randomly selected Americans is
1790, then test the hypotheses that Americans work significantly more than Danes based on this
sample mean. Use a level of significance of α = 0.05.
(2 pts)Formula
(2 pts)Substitution
(2 pts) z value
(2 pts)
(3 cpts) 3e. Based on the results in this study, do Americans work more than people in
Denmark?
Choose 1: Yes
p-value
No
http://www.vox.com/2014/5/9/5687204/this-proposal-to-fix-money-in-politics-is-so-crazy-itjust-might-work
http://www.fastcoexist.com/3029110/5-simple-office-policies-that-make-danish-workers-waymore-happy-than-americans