THE FINAL EXAM
MATH 311, SPRING 2005
JUNE 8, 2005
HELLO, MY NAME IS: _____________________________
________________________________________________________________________________________________________________
 ALL PERTINENT WORK MUST BE SHOWN NEATLY AND CORRECTLY. POINTS WILL BE DEDUCTED FOR INCORRECT, MISSING, OR
UNCLEAR WORK REGARDLESS OF THE FINAL ANSWER. COMPLETE ENGLISH SENTENCES MUST BE GIVEN FOR ALL “SHORT ANSWER” TYPE
QUESTIONS. DRAW A CIRCLE OR A BOX AROUND YOUR ANSWER.
Distribution of X:  X  np,  X  np(1  p)
z
x
z

( x1  x2 )  ( 1   2 )
n
1.
p
X 2
n4
p1 
X1  1
,
n1  2
Distribution of p :  p  p,  p 

2
1
n1
SE p 
p2 
X 2 1
,
n2  2
SE 

2
t
2
p(1  p)
n
( x1  x2 )  ( 1   2 )
2
2
s1 s2

n1 n2
n2
p(1  p)
n4
p1 (1  p1 ) p2 (1  p2 )
,

n1  2
n2  2
p
X1  X 2
,
n1  n2
SE 
1 1
p(1  p)   
 n1 n2 
(3 points each) Describe an explicit scenario for which the given test would be appropriate. BE SPECIFIC.
For example, if the question was “Describe a scenario in which a 2-sample t test would be appropriate, then a possible answer would
be this: A biologist is curious if the length of the mandible can used determine the sex of a jackal skeleton. Mandible lengths are
measured on several jackals (male and female) and the average lengths are compared.
a.
Describe a scenario in which a 1-sample t test would be appropriate.
b.
Describe a scenario in which a 2-sample t test would be appropriate (use an example different from the one above
c.
Describe a scenario in which a matched pair t test would be appropriate.
d.
Describe a scenario in which a two-population proportion test would be appropriate.
2.
3.
(4 points) Which of the following is likely to have a mean that is smaller than the median?
a.
The salaries of all National Football League players.
b.
The scores of students (out of 100 points) on a very easy exam on which most score perfectly, but a few do very poorly.
c.
The prices of homes in a large city.
d.
The scores of students (out of 100 points) on a very difficult exam on which most score poorly, but a few do very well.
(4 points) Is the mean height for all adult American males between the ages of 18 and 21 now over 6 feet? If the population of all
adult American males between the ages of 18 and 21 has a mean height of  feet and a standard deviation of  feet, to answer this
question one would test which of the following null and alternative hypotheses?
a. H0:  = 6 vs. Ha:  > 6.
b. H0:  = 6 vs. Ha:  < 6.
c. H0:  = 6 vs. Ha:   6.
d. H0:  = 6 vs. Ha:  = 6 ±
4.

n
, assuming our sample size is n.
(4 points) A study found a correlation of r = –0.61 between the gender of a worker and his or her income. You may correctly
conclude
a. women earn more than men on the average.
b. women earn less than men on the average.
c. an arithmetic mistake was made. Correlation must be positive.
d. this is incorrect because r makes no sense here.
5.
A sample was taken of the salaries of 20 employees of a large company. The following is a boxplot are the salaries (in thousands of
dollars) for this year.
a.
(4 points) Based on this boxplot, which of the following statements is true?
i. The maximum salary is between 60 and 70 thousand dollars.
ii. The minimum salary is 20 thousand dollars.
iii. The interquartile range is about 20 thousand dollars.
iv. The median salary is a little less than 40 thousand dollars.
b.
(4 points) Based on this boxplot, which of the following statements is true?
i. The salary distribution is fairly symmetric.
ii. About 10 employees make more than $50,000.
iii. Nobody makes more than $80,000.
iv. All of the above.
6.
(4 points) Twenty multiple choice questions are on an exam, each having responses a, b, c, or d. Suppose a student guesses the
answer to each question, and the guesses from question to question are independent. Let X be the number of questions for which the
student has the same answer as the person sitting next to him on his right. The distribution of X is
a. B(20, .2).
b. B(20, .25).
c. B(4, .25).
d. impossible to determine unless the student sitting next to him is also guessing.
7.
(4 points) A random sample of size 25 is to be taken from a population that is normally distributed with mean 60 and standard
deviation 10. The average J of the observations in our sample is to be computed. The sampling distribution of J is
a. normal with mean 60 and standard deviation 10.
b. normal with mean 60 and standard deviation 2.
c. normal with mean 60 and standard deviation 0.4.
d. normal with mean 12 and standard deviation 2.
8.
In a large Midwestern university (the class of entering freshmen being on the order of 6000 or more students), an SRS of 100
entering freshmen in 1993 found that 20 finished in the bottom third of their high school classes. Admission standards at the
university were tightened in 1995. In 1997, an SRS of 100 entering freshmen found that 16 finished in the bottom third of their high
school class. Let p1 and p2 be the proportion of all entering freshmen in 1993 and 1997, respectively, who graduated in the bottom
third of their high school classes.
Test these data to determine if the tighter requirements have resulted in better students.
a.
(2 points) Hypothesis tested:
Ho:
Ha:
b.
(6 points) Compute the p-value of these data:
c.
(2 points) What conclusion should the administrators make?
9.
Below are some data for members of the men's varsity sock-matching team. It is thought that perhaps there is a relation between the
member's GPAs and the number of credit hours taken during the quarter. The data are also recorded in columns C1 and C2 of
FINAL.MTW, which you should download now from http://www.cwu.edu/~englundt/Data.htm (if you haven't yet).
Credit
Hours
GPA
6
8
11
7
1
5
4
9
3
1
10
2
2.34
2.39
2.41
2.32
2.1
2.32
2.29
2.36
2.25
2.1
2.43
2.2
a. (3 points) If the number of credits taken is used to predict the expected GPA of the team members, which variable is the
explanatory variable and which is the response variable.
b. (3 points) Find the equation of the regression line for these data.
c. (3 points) How well does the regression line summarize the data? Use the appropriate quantifications.
d. (3 points) What GPA would you predict that an all-star sock-matcher would achieve if he took 18 credits?
10. (10 points) Because of the recent electricity crisis in California, the government and the utility companies have subjected the
citizens of California to a media campaign/onslaught in hopes of reducing their electricity usage. To measure the effectiveness of
their media blitz, they compiled the energy used (in kilowatt hours) in 20 homes both one month before and one month after the
campaign began. What do the data show about the effect of the campaign? Be specific, use the language and analysis tools we
have learned. Use every graphical and numerical summary that is appropriate and that we discussed in class to justify your claim.
Note: this question is intentionally open-ended – I’m testing the whole of what you’ve learned.
The data recorded below are also in the Minitab worksheet.
Before the
campaign
After the
campaign
380
283
361
487
321
349
447
407
366
402
383
427
356
480
375
420
356
350
434
477
410
384
403
392
329
316
393
430
399
325
426
339
345
360
406
410
465
431
318
326
11. All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of
our homes. High-frequency EM radiation is thought to be a cause of cancer; the lower frequencies associated with household
current are generally assumed to be harmless. To investigate this, researchers visited the addresses of children in the Denver area
who had died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the
building as either a high-current configuration (HCC) or as a low-current configuration (LCC). Here are some of the results of the
study.
Leukemia
52
84
HCC
LCC
a.
Lymphoma
10
21
Other Cancers
17
31
(4 points) Complete the following table:
Leukemia Lymphoma
Other
Cancers
HCC
52
10
17
LCC
84
21
31
Total
b.
(4 points) Compute χ2.
c.
(4 points) Compute the corresponding p-value.
d.
(3 points) What should the researchers conclude?
Total