Download Exam #2 - TAMU Stat

STAT303 Sec 508-510
Spring 2008
Exam #2
Form A
Instructor: Julie Hagen Carroll
Name:
1. Don’t even open this until you are told to do so.
2. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark your
answers clearly. Multiple marks will be counted wrong.
3. You will have 60 minutes to finish this exam.
4. 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.
5. 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.
6. When you are finished please make sure you have marked your CORRECT section (Tuesday 12:45 is 508, 2:20 is 509,
and 3:55 is 510) and FORM and 20 answers, then turn in JUST your scantron.
7. Good luck!
1
STAT303 sec 508-510
Exam #2, Form A
Spring 2008
1. The capacity of a brand of fish tank is normally dis6. Which of these statements is NOT true??
tributed with a mean of 15 Liters and a standard deviA. The distribution of the sample mean is always noration of 2 Liters. What proportion of fish tanks have a
mal with mean equal to the population mean and
capacity between 16 and 18.5 Liters?
standard deviation equal to the
√standard deviation
A. 0.27
of the population divided by n.
B. Two events A and B are independent if and only
B. 0.89
if P (A and B) = P (A) ∗ P (B).
C. 0.11
C. A p-value is the probability of obtaining an estiD. 0.73
mate as extreme or even more extreme that the
E. 0.69
one we observe.
2. Let p42 ∼ N (0.7, 0.0712 ). What is P (p42 < 0.5)?
D. All of the above are true.
E. None of the above are true.
A. 0.5
B.
C.
D.
E.
0
0.9976
0.0024
0.2
7. What are the z critical values, the zα/2 , for a 64% confidence interval?
A.
B.
C.
D.
E.
3. Using the three confidence intervals below, what is the
correct range of the p-value when testing H0 : µ = 13
vs. HA : µ 6= 13?
90% (5.943, 12.977)
95% (5.269, 13.651)
99% (3.952, 14.968)
A.
B.
C.
D.
E.
±0.36
±0.18
±0.92
±0.57
±0.74
8. Suppose you’re testing H0 : µ = 5 vs. HA : µ > 5
and you get a p-value = 0.036. Which of the following
is/are correct?
p-value > 0.10
0.10 > p-value > 0.05
0.05 > p-value > 0.01
p-value< 0.01
You need a test statistic value to determine the
p-value
A. 5 is NOT less than 3.6, so we fail to reject.
B. The true mean is significantly greater than 5 at
the 5% level.
C. We can’t say the true mean is significantly greater
than 5 at the 5% level.
D. We can’t say the true mean is significantly greater
than 5 at the 10% level.
E. Two of the above are correct.
4. Suppose we choose a student at random from a large
statistics class and we ask her how much time she spent
studying during the last 24 hrs. Which of the following
statements is TRUE?
9. What are the mean and median for the distribution
below?
A. The sample space is the discrete interval (0, 24).
B. The random variable is categorical.
C. We can approximate the distribution with the normal using the Central Limit Theorem.
D. All of A, B, and C are true.
E. All of the above are false.
X
| 1 | 2 | 3
| 4 | 5
-------------------------------------p(X) | 0.5 | 0.2 | 0.15 | 0.1 | 0.05
A.
B.
C.
D.
E.
5. A 95% confidence interval of 14 to 17 means that
A. 95% of the time the true mean will be between 14
and 17.
B. 95% of the confidence intervals calculated like this
one will contain the true mean.
C. 95% of the true means will be between 14 and 17.
D. All of the above are correct.
E. None of the above are correct.
µ=3
µ=2
µ=2
µ=2
µ=2
and
and
and
and
and
X̃
X̃
X̃
X̃
X̃
=3
= 1.5
=3
=2
=1
10. Using the distribution above, how likely are you to get
two 4’s OR a two 5’s if you sample randomly?
A.
B.
C.
D.
E.
2
0.0125
0.15
0.000025
0.005
0.0225
STAT303 sec 508-510
Exam #2, Form A
Spring 2008
2
11. Suppose we test the following: H0 : µ = 20 vs. 15. Let X ∼ N (25, 4 ). What is P (18 < X < 20)?
HA : µ > 20. Where µ is the mean tree height in feet
A. 0.0655
in Yosemite national park. 20 trees were randomly selected and measured. The p-value for the test statistic
B. 0.1457
was 0.23. Your boss wants to know what the number
C. 0.3085
0.23 means. It is
D. 0.0228
A. the probability that the null hypothesis is true.
E. 0.9772
B. the probability of making a Type I error.
16. Had we taken a sample of size, n = 25, from the popuC. the probability of making a Type II error.
lation above, what would the probability have been for
D. how many standard deviations your statistic was
X 25 ?
from the claimed parameter value of 20.
E. None of the above are correct.
A. More than for X, since more X’s are closer to the
mean, µ.
12. Given the hypothesis above with a p-value = 0.23,
which of the following would be a correct conclusion?
B. Less than for X, since less X’s would be that far
from the mean, µ.
A. Since 23 is greater than 20, we can conclude that
the alternative hypothesis is true.
C. Less than for X, since less X’s are above the mean,
µ.
B. Since the p-value is large, we can conclude that
the null hypothesis is true.
D. The same as for X, since the mean, µ is the same
for both.
C. Since the p-value is 0.23, there is a 23% chance
that the null hypothesis is true.
E. You can’t say without calculating the probability.
D. Since the p-value is 0.23, we have failed to prove
that the alternative hypothesis is true.
17. Why is the Central Limit Theorem so important in the
study of statistics?
E. Since the p-value is 0.23, we have failed to prove
that the alternative hypothesis is false.
A. It allows us to use the normal distribution for any
kind of data.
13. Let X 10 ∼ N (5, 62 ), n = 10. How large does the a
sample mean have to be to be in the TOP 10% of the
distributuion?
B. It tells us that any data can be approximately normal if we take a large enough sample.
C. It tells us that any sample mean can be approximately normal.
A. Since the sample is less than 30, we cannot calculate find this percentile.
B. 7.43
C. 12.68
D. 8.24
E. 5.6
D. It tells us that any sample mean will be unbiased.
E. None of the above are true statements of the CLT.
18. What is the sampling distribution of the sample proportion, p, if we sample 20 times from a population
with a true proportion of successes, π = 0.75?
14. Why do we call the distribution of the sample mean,
X n , a sampling distribution?
A. p20 ∼ N (0.75, 0.09682 )
B. p20 ∼ N (0.75, 0.0093752 )
C. µp = 0.75 and σp = 0.0968 but it’s not normal
since the sample size is less than 30
D. µp = 0.75 and σp = 0.009375 but it’s not normal
since the sample size is less than 30
E. None of the above are exactly true.
A. because it’s the distribution of the sample of random observations
B. because we must take a sample just to get one
random observation
C. because we sample from the distribution to find
the sample mean
D. because the distribution is only of a sample, not
the whole population
E. because we can’t get the distribution of the whole
population of sample means, only samples
3
STAT303 sec 508-510
Exam #2, Form A
19. The Survey of Study Habits and Attitudes (SSHA)
is a psychological test that measures the motivation,
attitude toward school, and study habits of students.
Scores range from 0 to 200. The mean score for U.S.
college students is about 115 with a standard deviation of about 30. A teacher who suspects that older
students have better attitudes toward school gives the
SSHA to 25 students who are at least 30 years of age.
This sample produces a mean score of 132.2. What set
of hypotheses should the teacher use to prove she is
correct about older students’ attitudes?
A.
B.
C.
D.
E.
H0
H0
H0
H0
H0
: µ = 132.2 vs. HA : µ 6= 132.2
: µ = 132 vs. HA : µ > 132.2
: µ = 115 vs. HA : µ 6= 115
: µ = 115 vs. HA : µ > 115
: µ = 132 vs. HA : µ > 115
20. Using the same scenario in the last question, which of
the following would be considered a Type I error?
A. The teacher concludes that older students are
smarter than the general population of U.S. students.
B. The teacher concludes that older students have
better attitudes than the general population of
U.S. students.
C. The teacher fails to prove that older students have
better attitudes than the general population of
U.S. students when actually their attitudes are
better.
D. The teacher concludes that older students have
better attitudes than the general population of
U.S. students when actually their attitudes are
better.
E. The teacher concludes that older students have
better attitudes than the general population of
U.S. students when actually their attitudes are not
any better.
21. Suppose we test the following: H0 : µ = 25 vs.
HA : µ 6= 25 and get a p-value = 0.067. Which of
the following is/are true?
A. 0.067 would be in a 95 and 99% confidence interval
for the mean if calculated from the same data.
B. We would conclude that the true mean is not 25
at the 10% significance level.
C. We would conclude that the true mean is 25 at the
5 and 1% significance levels.
D. All of the above are true.
E. Exactly two of the above are true.
1A,2D,3B,4E,5B,6A,7C,8B,9B,10A,11E,12D
13C,14B,15A,16B,17E,18E,19D,20E,21B
4
Spring 2008