Stat 301 B – Fall 2014 – Midterm exam 1
2 October 2014
Questions packet
Instructions:
1. Put your name on the back of the last page of the questions packet. I don’t want to see your
name until I have finished grading.
2. Read each question carefully and completely. Ask if you don’t understand something.
3. Answer each question and show work in the space provided. Scratch paper is provided for your
use, but I will only read and evaluate what you put in the answer spaces.
4. Use the JMP output. You do not need to calculate something that JMP has already calculated. I
am happy to answer questions along the lines of ‘(You pointing to a number on the JMP output)
Is this the estimate of the difference in means?’.
5. The exam has a total of 100 pts. Each question is worth 3, 4, or 5 points.
6. You can keep the Information packet and Formula sheet. Turn in the Questions packet.
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1. Dioxin in chemical plant workers.
a.
3 pts. Based on what you see in the histogram and/or box plot, what is the concentration of Dioxin
(approximately) in the typical worker at this chemical plant? Include units with your answer.
b. 4 pts. Is the distribution of Dioxin concentration symmetrical or skewed? Briefly explain your choice.
c. 4 pts. What is the standard error of the mean? (show your work, state what item in the JMP output
provided your answer, or state that you need additional information)
d. 3 pts. Describe, in a non-technical way (i.e., to someone who cares about chemical plant workers but
doesn’t known any statistics), how to interpret the standard error of the mean (i.e., explain what the se
“means”).
e. 4 pts. Dioxin is a nasty chemical. The company wants to be certain that the mean Dioxin
concentration in all 1550 workers is less than 500 ppt. Calculate the T statistic that tests the null
hypothesis that the mean Dioxin concentration equals 500 ppt. (show your work, you don’t need to
calculate a p-value)
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f. 4 pts. The two-sided p-value for the test in part e is 0.0245. What should you tell management when
they ask you how the mean Dioxin in all 1550 workers compares to the standard of 500 ppt?
g. 5 pts. The 95% confidence interval for the mean is (328, 488). Is it reasonable to conclude that 95%
of the workers at this chemical plant have Dioxin concentrations between 328 ppt and 488 ppt? Briefly
explain why or why not.
2. Oatmeal and blood pressure.
a. 4 pts. Calculate the pooled standard deviation, sp. (Show your work, state what item in the JMP
output provided your answer, or state that you need additional information)
b. 4 pts. How many degrees of freedom are associated with the pooled standard deviation, sp. (Show
your work, state what item in the JMP output provided your answer, or state that you need additional
information)
c. 5 pts. Is the pooled standard deviation an appropriate summary of the variability in each of the two
groups of men? Briefly explain why or why not.
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d. 4 pts. The report of this investigation includes the following table of sample averages:
Group
Sample size (N) Sample Average
eat oatmeal
20
117.067
hate oatmeal
42
126.213
Are the averages in this table appropriately reported? Briefly explain your answer.
e. 4 pts. What is the 95% confidence interval for the difference in means? (Show your work or state
what item in the JMP output provided your answer)
f. 4 pts. Based on what you see in the JMP output, what can you say about the p-value for the test of
the null hypothesis that the mean difference = 0? Briefly explain your answer.
g. 5 pts. Are these data paired or are they two independent samples? Briefly explain your choice.
h. 5 pts. Is it appropriate to conclude that eating oatmeal three times a week or more will reduce your
blood pressure? Briefly explain why or why not.
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3. PCB and egg shell thickness
a) 4 pts. What egg shell thickness do you expect to find if the PCB concentration in the egg = 0? (Show
your work, state what item in the JMP output provided your answer, or state that you need additional
information.)
b) 4 pts. Give a 95% interval that describes the average egg shell thickness in a large collection of eggs,
all with a PCB concentration = 0. (Show your work, state what item in the JMP output provided your
answer, or state that you need additional information.)
c) 4 pts. What is the p-value for the test of the null hypothesis that the regression slope = 0? (Show your
work, state what item in the JMP output provided your answer, or state that you need additional
information.)
d) 5 pts. Based on your result in question 3c, is it appropriate to conclude that “The regression slope for
Brown Penguins on Anacapa Island = 0?”. Briefly explain your answer.
e) 4 pts. What is the 95% confidence interval for the difference in average shell thickness between eggs
with a PCB concentration of 225 ppb and eggs with a PCB concentration of 226 ppb? (Show your work,
state what item in the JMP output provided your answer, or state that you need additional information.)
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f) 4 pts. If the shell of an egg is thin, it is more likely to get broken during incubation. What 95% interval
describes the uncertainty in predicted egg shell thickness for a single egg with a PCB concentration of
350 ppb? (Show your work, state what item in the JMP output provided your answer, or state that you
need additional information.)
g) 4 pts. The investigators made sure they had only one egg from each nest and only one measurement
of PCB concentration per egg. Would you be concerned if the data set had 3 measurements of PCB
concentration for each egg, i.e., a total of 195 observations? Briefly explain your concern or lack of
concern.
h) 3 pts. Do you have any concern about lack of fit of the regression line, i.e. the assumption that the
relationship between PCB concentration and mean egg thickness can be described by a straight line?
Briefly describe what in the output indicates a concern or lack of concern.
i) 3 pts. Do you have any concerns about the assumption of equal variances? Briefly describe what in
the output indicates a concern or lack of concern.
j) 3 pts. Do you have any concerns about the assumption that the errors are normally distributed?
Briefly describe what in the output indicates a concern or lack of concern.
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