Download STAT303 Sec 504-6 Fall 2015 Exam #2 Form A

STAT303 Sec 504-6
Fall 2015
Exam #2
Form A
Instructor: Julie Hagen Carroll
Name:
1. Don’t even open this until you are told to do so.
2. Remember to turn your phone off now.
3. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark your
SINGLE answer clearly. Multiple marks will be counted wrong.
4. You will have 50 minutes to finish this exam.
5. If you have questions, please write out what you are thinking on the back of the page so that we can discuss it after
I return it to you.
6. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade of zero on the
exam. You must work alone.
7. When you are finished please make sure you have marked your and FORM and 20 answers, then turn in JUST your
scantron. KEEP your EXAM.
8. Good luck!
1
STAT303 sec 504-6
Exam #2, Form A
Fall 2015
R
1. If the true proportion of Snickers in a typical kid’s
6. A recent article on Consumerist.com reported, “The
Trick or Treat bag is 40%, what is the smallest number
average middle-class American only has $20,000 saved
of pieces of candy needed in a bag to use the normal
for retirement.” Suppose a 95% confidence interval for
approximation to determine whether a particular kid
the average amount middle-class Americans had saved
didn’t get the right amount?
for retirement was ($15,000, $25,000). How would we
interpret this interval in context?
A. 30
A. I am 95% confident that the middle-class AmerB. 40
icans in the sample had between $15,000 and
C. 25
$25,000 saved for retirement, on average.
D. 37
B. I am 95% confident that all middle-class AmerE. 38
icans have an average of between $15,000 and
2. So, if the true proportion of healthy stuff, like apples,
$25,000 saved for retirement.
in a Halloween bag is 30% of 100 things (candy, toys,
C. I am 95% confident that 95% of all middleetc.), how many healthy things does a kid have to get
class Americans have between $15,000 and $25,000
(out of 100), to feel cheated which I’ll define as the top
saved for retirement.
5%?
D. There is a 95% chance that the average amount all
middle-class Americans have saved for retirement
A. 100 ∗ (0.3 + 1.645 ∗ 0.0458) = 37 or 38
is between $15,000 and $25,000.
B. 100 ∗ (0.3 + 1.96 ∗ 0.0458) = 39
E.
There is a 95% chance that the average amount the
C. 100 ∗ (0.3 + 0.95 ∗ 0.0458) = 34 or 35
middle-class
Americans in this sample have saved
D. 100 ∗ (0.3 ∗ 0.95) = 28 or 29
for
retirement
is between $15,000 and $25,000.
E. Any at all is a rotten neighborhood.
7. What’s more popular for Halloween, dressing up as a
superhero or a villian? Ignoring any other type of costume (don’t count them in your sample), which of the
following set of hypotheses should you use to prove superheroes are more popular? S is for superhero, V is
for villian
3. A study involved measuring the average IQ of Americans. What does the Central Limit Theorem say about
the study? As long as the sample size n is large enough:
A. The number of Americans in the study will be normally distributed.
B. The average IQ of all Americans will be normally
distributed.
C. The IQ scores of Americans in the sample will be
normally distributed.
D. The IQ scores of all Americans will be normally
distributed.
E. The average IQ of Americans in the sample will
be normally distributed.
A.
B.
C.
D.
E.
: pS = 0.5 vs. HA : pS 6= 0.5
: pS = 0.5 vs. HA : pS > 0.5
: pS = pV vs. HA : pS > pV
: pS < pV vs. HA : pS ≥ pV
: µS = µV vs. HA : µS > µV
8. Say you tested H0 : µS = µV vs. HA : µS > µV
where µS is the average number of superheroes this
Halloween and µV is the average number of villians.
Even though this would be a two-sample test, the rules
are the same, so knowing what you do about hypothesis testing, which of the following could you NOT!!!!!!
prove?
4. Assume X ∼ N (14, 82 ). How likely are you to get a
negative average (0 or below) based on 10 observations?
n = 10
A. You can’t have negative numbers in a normal distribution.
B. 10 is not a big enough sample to use the Z table
to find the probability (not normal).
C. 0
D. 0.0401
E. 1.75
A. the average number of villians is more than that
of superheroes
B. the average number of villians is the same as that
of superheroes
C. the average number of villians is less than that of
superheroes
D. None of the above are provable with this set of
hypotheses.
E. Two of the above are not provable with this set of
hypotheses.
5. What does conservative mean in Statistics? Hint: less
risky
A.
B.
C.
D.
E.
H0
H0
H0
H0
H0
a wider confidence interval
making H0 harder to reject
rounding up so the sample size is larger
All of the above are correct.
Only two of the above are correct.
2
STAT303 sec 504-6
Exam #2, Form A
Fall 2015
9. You want to know if the true proportion of chocolate 12. Which of the following affect the width of a confidence
candy in a typical Halloween bag is 50% or not but all
interval for the true population mean?
you’re given is a 95% confidence interval for p based on
A. the sample size
a random sample of bags with 50 pieces of candy each.
B. the sample mean
If the interval is (0.53, 0.73), what can you say?
C. the population mean
A. It is plausible that the true proportion is only 50%.
D. whether the sample is biased or not
B. It is plausible that the true proportion is 60%.
E. Two of the above affect the width.
C. It is plausible that the true proportion is as much
13. So Elsa from the Disney movie F rozen is still a very
as 75%.
popular Halloween costume (and not just for kids).
D. All of the above are plausible.
Your friend says the internet claims 25% of the cosE. Your mom got to into your bag after she sent you
tumes for females this year are Elsa. You can’t believe
to bed and ate most of the chocolate.
it’s the high, so you check with your local costume shop
10. Just before the recession of 2007, 48% of Americans
and find that 12 of the 90 female costumes sold where
said that it was a good time to find a quality job.
Elsas. What is your test statistic value and it’s P-value?
That percentage dipped, but a researcher is interested
A. You need at least 30 costumes to be Elsas to use
in whether in 2014 the percentage was still lower than
the normal approximation.
it was in 2007. For testing H0 : p = 0.48 vs. Ha : p <
B.
You need at least 15 costumes to be Elsas to use
0.48, where p = proportion of Americans in 2014 that
the
normal approximation.
think now is a good time to find a quality job, a P-value
C.
z
=
−3.39 P-value= 0.0003
of approximately 0 was found from a sample of over a
D.
z
=
−2.63 P-value= 0.0043
thousand randomly selected Americans, with a sample
E.
z
=
−3.39 P-value= 0.0006
proportion of 0.31. How can we interpret this P-value
in context?
14. The population average number of pieces of candy in
a regular kid’s Halloween bag is 98 with a standard
deviation of 7. In a typical neighborhood of 35 houses,
the average was 105 pieces with a standard deviation of
5. Assuming all neighborhoods of 35 houses is normally
distributed, what is the sampling distribution of the
sample mean based on 35 houses?
A. There is approximately no chance that the proportion of all Americans that think now is a good
time to find a qualtiy job is equal to 0.48.
B. There is approximately no chance that the proportion of Americans in the sample that think now is
a good time to find a qualtiy job is equal to 0.48.
C. There is approximately no chance that the proportion of all Americans that think now is a good
time to find a qualtiy job is less than 0.48.
D. There is approximately no chance that we would
have found a sample proportion of 0.31 or smaller,
if in reality 48% of Americans today think it is a
good time to find a quality job.
E. There is approximately no chance that we would
have found a sample proportion of 0.48 or smaller,
if in reality 31% of Americans today think it is a
good time to find a quality job.
A.
B.
C.
D.
E.
N (98, 72 )
N (105, 52 )
N (98, 1.182 )
N (105, 0.8452 )
N (98, 0.8452 )
15. The hypotheses H0 : µ = 350 vs HA : µ 6= 350 are
examined using a sample of size n = 20 with mean =
358 and standard deviation = 15. What is the P -value
of this test if we assume that the data is normal?
A.
B.
C.
D.
E.
11. Suppose in the previous problem only 500 Americans
were in the sample (n decreases), but everything else
was the same. Which of the following would be true
about the P-value and conclusion?
A. Since the proportions are the same, nothing would
change.
B. You would need to run another hypothesis test to
determine them.
C. The P-value would be smaller since the sample size
is smaller and the null would be less believable.
D. The P-value would be larger since the sample size
is smaller and the null would be more believable.
E. The P-value would be smaller since the sample size
is smaller and the null would be more believable.
3
0.0084
0.0168
0.025 > P -value > 0.02
0.02 > P -value > 0.01
0.04 > P -value > 0.02
STAT303 sec 504-6
Exam #2, Form A
Fall 2015
16. Same situation - H0 : µ = 350 vs HA : µ 6= 350 are 19. A recent Gallup poll reported that 70% of Americans
examined using a sample of size n = 20 with mean
favor using federal money for preschool education, but
= 358 but say the P-value was 0.086. Which of the
you think it’s actually higher than that. To help prove
following is true?
your point, here are three confidence intervals for the
proportion of all Americans who favor federal funding
A. 350 would fall within a 90 and 95% but not a
of preschools are shown below. What is a range for the
99% confidence interval for the true mean using
P-value of a test of hypotheses of H0 : p = 0.75 vs.
the same data.
Ha : p 6= 0.75?
B. 358 would fall within a 90 and 95% but not a
99% confidence interval for the true mean using
90%: (0.676, 0.723)
the same data.
95%: (0.672, 0.728)
C. 350 would fall within a 95 and 99% but not a
99%: (0.663, 0.737)
90% confidence interval for the true mean using
the same data.
A. P -value > 0.10
D. Two of the above are true.
B. 0.10 > P -value > 0.05
E. None of the above are true.
C. 0.05 > P -value > 0.01
D. P -value< 0.01
17. Suppose I tested H0 : µ ≤ 5 vs. HA : µ > 5 with a
E. The answer cannot be determined without the
sample mean, x̄ = 7, sample size, n = 20 and stansample size n.
dard deviation, s = 4 from a normal population. What
would cause me to be LESS LIKELY to reject? Holding 20. Ok, you really needed the P-value for the greater than
all other variables constant.
test, so let’s say it is 0.034 (don’t worry, this number has
absolutely nothing to do with the previous question).
Which of the following is the correct conclusion?
A.
B.
C.
D.
a larger sample standard deviation
a larger sample mean
a larger hypothesized value µ0
All of the above would have a larger P -value, so I
would be less likely to reject.
E. Only two of the above would have a larger P -value,
so I would be less likely to reject.
A. Since the P-value = 0.034 is less that 5%, we would
reject and claim that the true proportion of Americans in favor is more than 75%.
B. Since the P-value = 0.034 is less that 5%, we would
reject and claim that the true proportion of Americans in favor is 75%.
C. Since the P-value = 0.034 is less that 5%, we would
fail to reject and claim that the true proportion of
Americans in favor is 75%.
D. Since the P-value = 0.034 is less that 5%, we would
fail to reject and claim there is not enough evidence to prove the true proportion of Americans
in favor is more than 75%.
E. The correct P-value would be 0.068, so we would
fail to reject and claim there is not enough evidence to prove the true proportion of Americans
in favor is more than 75%.
18. The P-value for the previous problem is 0.0188. What
does this mean? If I repeatedly sampled from this same
population,
A. a sample mean of 5 or more would happen less
than 2% of the time.
B. a sample mean of 5 or more would happen less
than 2% of the time if the true mean was 7.
C. a sample mean of 7 or more would happen less
than 2% of the time if the true mean was 5.
D. a sample mean of 7 would happen less than 2% of
the time if the true mean more than 5.
E. only 2% of the time would the sample mean be
greater than the true mean.
1E,2A,3E,4C,5D,6B,7B,8E,9B,10D,11D,
12A,13D,14C,15E,16C,17E,18C,19D,20A
4