Math 116 – Makeup Exam 3
Name:________________________________________
TIME YOURSELF. NO MORE THAN 15 MINUTES PER PAGE!
Q1. The Dairy Fresh Ice Cream plant in Greensboro, Alabama, uses a filling machine for its 64-ounce cartons. There is
some variation in the actual amount of ice cream that goes into the carton. The machine can go out of adjustment and
put a mean amount either less or more than 64 ounces in the cartons.
The manager thinks the machine is out of adjustment and to test his claim he selects a simple random sample of 16 filled
ice cream cartons. The sample data are:
62.7,
64.7,
64.0,
64.5,
64.6,
65.0,
64.4,
64.2,
64.6,
65.5,
63.6, 64.7,
64.0,
64.2,
63.0,
63.6
Test the manager’s claim at the 5% significance level.
(Assume all conditions are met in order to run one of the tests learned in class)
a) Write the relevant sample statistics (use your calculator to find them)
[2 points]
b) Write the hypotheses
[2 points]
c) Sketch the graph, shade and label possible locations of sample statistic
[2 points]
d) What test will you use in the calculator? T or Z? Why?
[2 points]
e) Run the test in the calculator and write the results
[2 points]
f) Does the data suggest that the machine is out of adjustment? YES, NO, EXPLAIN
[3 points]
g) Will the conclusion be different using a different significance level? YES, NO, EXPLAIN
[3 points]
Show complete and organized work below – label parts (a) – (g)
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Q2. The testing Center in Southern California creates standardized exams for a variety of quantitative disciplines,
including business statistics. Recently the Testing Center received complaints from faculty who have used its latest
business statistics test saying the mean time required to complete the exam exceeds the advertised mean of 40 minutes.
Before responding, employees at the Testing Center select at random the results of 100 business statistics students and
observe a sample mean x-bar of 43.5. Based on previous studies, suppose that the population standard deviation is
known to be sigma = 8 minutes.
a) Use a feature of the calculator to construct a 99% confidence interval estimate for the mean time required to
complete the exam.
[4 points]
b) Use the interval results to find the margin of error. Show work
[3 points]
c) Interpret the interval in words within context
[4 points]
d) What does the interval suggest?
[3 points]
a. The mean time may be equal to 40
b. The mean time is more than 40
c. The mean time is less than 40
e) Use the interval results and VERY CLEARLY explain your choice to part (d)
[4 points]
f) Should the Center in Southern California modify the standardized test of Business Statistics?
[4 points]
YES
NO
WHY?
Show complete and organized work below – label parts (a) – (f)
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Q3. Ten different families are tested for the number of gallons of water a day they use before and after viewing a
conservation video.
After
34 28 25 28 35 33 31 28 35 33
At the 0.05 significance level, test the claim that the mean number of gallons of water used a day is higher before than
after viewing the video. (Assume all conditions are met in order to run one of the tests learned in class)
a) Are the samples matched pairs (dependent) or independent samples?
[2 points]
b) Set both hypotheses. Sketch graph, shade rejection region, label, and indicate possible locations of the point
estimate in the graph.
[4 points]
c) Use a feature of the calculator to test the hypothesis. Indicate the feature used and the results
[4 points]
d) Was the video effective in reducing the number of gallons of water a day that families use?
YES
NO
EXPLAIN
[4 points]
e) Construct a 90% confidence interval for the mean difference of the number of gallons of water a day people use
[4 points]
Show complete and organized work below – label parts (a) – (e)
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Q4. Do two-month-old baby girls have on average, smaller head circumference than 2-month-old baby boys? A
researcher selects a simple random sample from each group and obtains the following results.
Sample size
Sample Mean
50
50
40.05
41.1
girls
boys
Sample Standard
deviation
1.64
1.5
Test the claim at the 1% level of significance. Assume the variable is normally distributed in both populations.
a) Find the point estimate for
b)
c)
d)
e)
f)
1  2
Write the hypotheses
Sketch the graph, shade and label possible locations of the point estimate
Run the test in the calculator and write the results
Write the conclusion within context
Will the conclusion be different using a different significance level? YES, NO, EXPLAIN
g) Construct a 98% confidence interval to estimate for 1  2 .
h) What does the interval suggest? Explain clearly based on interval results
Show complete and organized work below – label parts (a) – (h)
[2 points]
[2 points]
[2 points]
[2 points]
[3 points]
[3 points]
[3 points]
[3 points]
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Q5. In 1965, about 44% of the U.S. adult population had never smoked cigarettes. A national health survey of 1205 U.S.
adults (presumably randomly selected) during 2006 revealed that 615 had never smoked cigarettes.
Suppose you wished to test whether there has been a change since 1965 in the proportion of U.S.
adults that have never smoked cigarettes.
A) Which of the following are the appropriate hypotheses?
[3 points]
H o : p  0.51
H o : p  0.51
H o : p  0.44
H o : p  0.44
H o : p  0.51
H a : p  0.51
H a : p  0.44
H a : p  0.44
H a : p  0.44
H a : p  0.51
B) Sketch the graph, shade and label the sample statistic in the graph
[2 points]
C) Run the test in the calculator and write the results
[3 points]
D) Write the conclusion to the problem within context
[4 points]
E) Does the conclusion depend of the significance level? YES
F) Which of the following represents the p-value? Circle one
NO
EXPLAIN
[4 points]
[4 points]
p = P(p-hat < 0.44)
p = P(p-hat > 0.44)
p =2* P(p-hat > 0.44)
p = P(p-hat < 0.51)
p = P(p-hat > 0.51)
p =2* P(p-hat > 0.51)
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Q6. Suppose we want a 90% confidence interval for the average amount of time (in minutes) spent per week on
homework by the students in a large introductory statistics course at a large university. The interval is to have a margin
of error of 2 minutes, and the amount spent has a normal distribution with standard deviation sigma = 30 minutes. The
sample size required to accomplish this should be _________________ Show work.
[5 points]
Q7. ACCUPRIL - Accupril, a medication supplied by Pfizer Pharmaceuticals, is meant to control hypertension. In
clinical trials of Accupril, 2142 subjects were divided into two groups. The 1563 subjects in Group 1 (the experimental
group) received Accupril. The 579 subjects in Group 2 (the control group) received a placebo. Of the 1563 subjects in the
experimental group, 61 experienced dizziness as a side effect. Of the 579 subjects in the control group, 15 experienced
dizziness as a side effect.
I constructed a 95% confidence interval estimate for the difference between the proportions experiencing dizziness in
the experimental group and in the control group. This is the interval obtained:
- 0.003 < p1 – p2 < 0.02923
A) What feature of the calculator did I use to obtain the interval?
[2 points]
B) Use the interval results to answer: What does this interval suggest?
Circle one of the given options (a), (b), or (c) below
a) It’s possible that p1 and p2 are equal
b) p1 is actually lower than p2
c) p1 is actually higher than p2
[3 points]
C) MUST EXPLAIN VERY CLEARLY your choice to part (A)
[4 points]
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