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Unformatted text preview: Practice for Exam 2
STAT 350 – Fall 2008
Exam 2
Your Name: ____________________________________ Your Seat: __________
Section Time (circle): 10:30 12:30 1:30 Note:
• You are responsible for upholding the Honor Code of Purdue University. This includes
protecting your work from other students.
• Show your work on all questions. Unsupported work will not receive full credit. Credit
will not be given for dumb luck. Showing work includes defining any random variable or
event you use in the solution. Showing work also includes identifying any named
distribution you are using the solution and the values of all relevant parameters.
• Decimal answers should be exact or to at least four significant digits.
• Unless otherwise stated, assume the significance level for any hypothesis test is 0.05.
• Standard Normal (Z) and values/probabilities must be taken from the tables provided.
Probabilities, pvalues, critical values, etc., for χ2, t, and F distributions must also be
taken from the tables provided.
• You are allowed the following aids: a onepage (8.5×11 inch) cheat sheet, a scientific
calculator, and pencils.
• Turn off and put away your cell phone before the exam begins! Question Points Possible Points Missed
1
27
2 8 3 21 4 28 5 6 6 10 Total 100 1. ETS (the company that administers the SAT) will endorse a SAT preparation course only if
there is substantial evidence that the course will increase a student's score by at least 30
points. Contracted by ETS, you wish to evaluate a new SAT prep course, so you find 20
volunteer high school juniors. You randomly select 10 of the volunteers to take prep course,
which you pay for (the rest of the volunteers get no preparation). You also pay for all 20
volunteers to take the SAT. You obtain the following summary data:
xc = 1343,
xn = 1278,
sc = 68,
s n = 72
The subscript "c" denotes those taking the SAT preparation Course and the subscript "n"
denotes the group those Not taking the prep course. Assume that the populations do have the
2
same underlying variance (that is, σ c2 = σ n ).
a. (5 points) Let μc denote the true mean SAT score of the population of students who
would take this SAT prep course and let μn denote the true mean SAT score of the
population of students who do not take this prep course. If the null hypothesis
is H 0 : μc − μn = 30 , state the appropriate alternative hypothesis for this test in terms of μc
and μn. b. (3 points) How many degrees of freedom are there for the test statistic? df = _________
c. (5 points) Find the critical value for this test (α = 0.05), and sketch the rejection region. d. (6 points) Find the value of the appropriate test statistic. e. (4 points) Find the pvalue of this test. f. (4 points) Based on your analysis, should ETS endorse this SAT prep course? Just
answer "yes" or "no". STAT 350 Exam 1 Page 2 of 2 2. (8 points; 2 points each) Multiple Choice. For each part, circle the single most appropriate
answer from the options provided.
a. Assume that you are tested H0: μ = 5 versus Ha: μ > 5 at α = 0.05 and you rejected the
null hypothesis. If you had used the same data to instead test H0: μ = 5 versus Ha: μ ≠ 5
at α = 0.05, would you have also rejected the null hypothesis?
(i) definitely yes
(ii) definitely no
(iii) maybe
b. Assume that you are tested H0: μ = 5 versus Ha: μ > 5 at α = 0.05 and you rejected the
null hypothesis. If you had used the same data to instead test H0: μ = 5 versus Ha: μ > 5
at α = 0.10, would you have also rejected the null hypothesis?
(i) definitely yes
(ii) definitely no
(iii) maybe
c. Assume that you are tested H0: μ = 5 versus Ha: μ > 5 at α = 0.05 and you rejected the
null hypothesis. If you had used the same data to instead test H0: μ = 5 versus Ha: μ > 5
at α = 0.01, would you have also rejected the null hypothesis?
(i) definitely yes
(ii) definitely no
(iii) maybe
d. Assume that you are testing H0: μ = 5 versus Ha: μ ≠ 5 at α = 0.05 and you rejected the
null hypothesis. Assume also that you found that x was greater than 5. If you had used
the same data to instead test H0: μ = 5 versus Ha: μ > 5 at α = 0.05, would you have also
rejected the null hypothesis?
(i) definitely yes
(ii) definitely no
(iii) maybe STAT 350 Exam 1 Page 3 of 3 3. Lesser Snow Geese come in two color variants, white and blue. The color is controlled by a
single gene with the blue being dominant to the white. So the offspring of two white parents
will all be white. Scientist studying imprinting in birds wanted to know if the color of a birds
parents affected the birds' matechoice (these geese mate for life). That is, do birds raised by
white parents have a preference for white mates over blue mates (or maybe opposites attract
and they might have a preference for blue mates). To control for the effects of the gosling
(baby goose) color, color of siblings, and noncolor genetic effects, the researchers took 40
eggs from the nests where both parents were white and gave one egg each to be raised by
"foster" parents that were either both white (20 eggs) or both blue (20 eggs). The next year
when the study goslings had reached sexual maturity, they recorded the color of each bird's
mate. The data is summarized in the table below. parent color mate color
white blue
white 15 5 blue 8 12 a. (8 points) Give a table of the expected values (counts). parent color mate color
white blue
white blue b. (5 points) What is the value of the test statistic (chisquare) for this data? c. (4 points) What is the pvalue for this test? Give as accurately as possible. d. (4 points) Based on your analysis above, what is your conclusion? Does the color of a
bird’s parents affect the bird’s matechoice? Just answer "yes" or "no"? STAT 350 Exam 1 Page 4 of 4 4. Tomato yield weight was compared in plants given one of three different formulations of
fertilizers. Eleven plants were used for each fertilizer treatment. The results are summarized
in the table below.
si
xi
A 97.9 14.9
B 109.7 17.3
C 86.3 21.6
a. (20 points) Conduct an analysis of variance, summarizing your results in the ANOVA
table outlined below (space to show relevant work is given below the table).
Source
Sums of Squares
Mean Squares
df
F
Fertilizer
Error
Total b. (4 points) Give the critical value for this test (α = 0.05). c. (4 points) Based on your analysis above, you would conclude (circle your choice):
(i) There is NO statistically significant difference in the mean tomato yield weight
among these three fertilizers
(ii) There IS a statistically significant difference in the mean tomato yield weight for at
least one of these fertilizers.
STAT 350 Exam 1 Page 5 of 5 5. (6 points; 2 points each) Children were given a number of different vegetables and asked to
rate them on a scale of 1 to 10 on taste (10 is best tasting, 1 is the worst). Using ANOVA,
the researchers found that the preferences (ratings) for these vegetables were not all the
same, so they conducted a Tukey Multiple Comparison (α = 0.05) to determine which
vegetables children had significantly different preferences for. The results of the Tukey
Multiple Comparison procedure are summarized below.
lima
beans
1.23 beets
1.35 spinach
2.46 brussel
sprouts
3.74 asparagus
4.13 broccoli
5.12 tomatoes
6.91 carrots
8.34 a. Children's preference for brussel sprouts was significantly different
from their preference for broccoli (circle). Yes No b. Children's preference for brussel sprouts was significantly different
from their preference for beets (circle) Yes No c. Children's preference for asparagus was significantly different from
their preference for broccoli (circle) Yes No 6. (10 points) You hear a news clip reporting that a recent study found that students with
parents who smoke do worse in school. You decide to examine the original paper. You see
that they randomly selected a large number of students in a range of grade levels and
obtained their grades and contacted each student's parents to determine whether at least one
of the parents smoked. At each grade level they had a large number of students with parents
that smoked and parents that did not smoke. At each grade examined, the average difference
between children of smokers and children of nonsmokers was at least half a grade (≥0.5
grade points) and the pvalues were all less than 0.01.
The newscaster that covered this study concluded her story stating, "This should serve as one
more reason for parents to quit smoking – your children will do better in school if you do."
Based on the information provided, do you agree with the newscaster's conclusion? Be sure
to support your answer using clear and complete sentences. STAT 350 Exam 1 Page 6 of 6 ...
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