Numeric Variable
1. The serum bilirubin level of 10 randomly selected patients admitted to a hospital for treatment
of hepatitis was taken.
a. Using the data in the file serum.jmp found on the course website construct a 99%
confidence interval for the population parameter of interest.
15.60 ≤ µ ≤ 23.94
b. Interpret the confidence interval found in part a.
99% confident the true mean serum bilirubin level of patients is between
15.60 and 23.94.
2. The maximum voluntary ventilation value for apparently healthy college seniors was recorded.
The data are summarized in the JMP output given below.
a. Looking at the histogram, describe the shape (or distribution) of the maximum voluntary
ventilation values.
Symmetric
b. The mean will most likely be __________ than the median.
i. Smaller
ii. The same
iii. Larger
c. Give the Five Number Summary for the maximum voluntary ventilation values.
Min
Q1
Med
Q3
Max
21
64
109
163.75
203
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d. Give the variance for the maximum voluntary ventilation values. Make sure to use the
appropriate statistical notation.
S2 = 56.302 = 3169.69
e. Looking at the boxplot, are there any potential outliers? Explain.
No because there are no dots on the plot.
f.
The middle 95% of maximum voluntary ventilation values falls between 21 and 203 .
g. Compute the range for the maximum voluntary ventilation values.
Range = 203 – 21 = 182
3. Previous research has found that the average height of European White Birch trees is 50 feet
with a standard deviation of 20 feet. It has also been found that the average height of Red
Maple trees is 75 feet with a standard deviation of 16 feet. Would it be more unusual to see a
European White Birch tree that is 75 feet tall or a Red Maple tree that is 43 feet tall? Make sure
to justify your reasoning.
zbirch =
75 - 50
= 1.25
20
z maple =
43 - 75
= -2
16
A Red Maple tree that is 43 feet tall because its z-score is further from the mean (i.e.
0) which makes it more unusual.
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4. A past study claimed that adults in America spend an average of 18 hours a week on leisurely
activities. A researcher wanted to test this claim and took a random sample of 14 people and
recorded the amount of time (in hours) they spend on leisurely activities which can be found in
the file leisure.jmp on the course website. Using JMP, carry out the hypothesis test to answer
the research question given below. Make sure to clearly state the hypotheses, condition(s), test
statistic, p-value, and conclusion in context.
Research Question – Is there evidence the amount of time adults in America spend on
leisurely activities has changed?
H0: µ = 18
Ha: µ ≠ 18
Condition:
1. N = 14 < 30 X
2. Reasonable to assume normal distribution? No X
3. Symmetric? YES √
Test statistic = 28
p-value = 0.0813
No evidence that the average time spent on leisurely activities is different from 18
hours.
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5. Psychology experiments sometimes involve testing the ability of rats to navigate mazes. The
mazes are classified according to difficulty, as measured by the mean length of time it takes rats
to find food at the end. One researcher needs a maze that will take rats an average of about
one minute (60 seconds) to solve. He tests one maze on several rats and the data can be found
in the file rat_maze.jmp on the course website.
a. Construct a 90% confidence interval for µ, the true mean time it takes rats to complete
the maze.
48.45 ≤ µ ≤ 54.37
b. Based on the confidence interval constructed in part a, is the maze the researcher
constructed suitable for the experiment? Explain
No because 60 is not contained in the interval, i.e. it’s not a possible value for
the mean time.
6. A clean air standard requires that vehicle exhaust emissions not exceed specified limits for
various pollutants. Many states require that cars be tested annually to be sure they meet these
standards. Suppose state regulators double check a random sample of cars that a suspect repair
shop has certified as okay. They will revoke the shop’s license if they find significant evidence
that the shop is certifying vehicles that do not meet standards.
a. Set up the null and alternative hypotheses the state regulators would test in this
situation.
H0: Vehicles certified meet the standards
Ha: Vehicles certified do not meet the standards.
b. Describe a Type I error in context for this situation.
Concluding that the vehicles certified do not meet the standards when they
really do.
c. Describe a Type II error in context for this situation.
Concluding the vehicles certified meet the standards when they really do not.
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7. It is believed that a person’s height should be the same as their wingspan. This was
demonstrated in the famous sketch by Leonardo Da Vinci called the Vitruvian Man.
Using the data set Vitruvian_Man.jmp found on the course website, answer the following
research question. Make sure to provide a detailed sketch or paste your JMP output below.
Research Question – Is there evidence that a person’s wingspan and height are not the same?
Difference = Height – Wingspan
H0: µd = 0
Ha: µd ≠ 0
Condition: npairs = 40 ≥ 30√
Test Statistic = t =
-0.81 - 0 -0.81
=
= -2.77
1.84
0.29
40
p-value = 0.0085
Evidence that a person’s wingspan and height are not the same.
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8. Facebook games have become very popular in the last year. It seems as though everyone is
playing at least one game on Facebook. One of the questions on the Student Data survey asked
about whether an individual plays Facebook games. Another question on the survey asked how
much time a person spends studying in a day (in minutes). Using the data Facebookstudying.jmp found on the course website, answer the following research question. Make sure
to provide a detailed sketch or paste your JMP output below.
Research Question – Is there evidence that a person who plays Facebook games spends less time
on average studying than someone who does not play Facebook games?
H0: µYes ≥ µNo
Ha: µYes < µNo
Condition: nyes = 74 ≥ 30 and nno = 251 ≥ 30√
Test statistic = t =
10.277
= 0.99
10.374
p-value = 0.8387
No evidence that a person who plays Facebook games spends less time on average
studying that someone who does not play Facebook games.
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9. The Ohio Environmental Protection Agency used the Index of Biotic Integrity (IBI) to measure
the biological condition, or “health” of an aquatic region. The IBI is the sum of metrics that
measure the presence, abundance, and health of fish in the region. Higher values of the IBI
correspond to healthier fish populations. Researchers collected IBI measurements for sited
located in difference Ohio river basins. (Journal of Agriculture, Biology, and Environmental
Sciences, June 2005) The data collected from the Muskingum and Hocking river basins obtained
is in the file IBI.jmp found on the course website.
Research Question – Is there evidence the mean IBI values differ for the two river
basins?
H0: µmuskingum = µhocking
Ha: µmuskingum ≠ µhocking
Condition: nmusingum = 53 ≥ 30 and nhocking = 51 ≥ 30√
Test statistic = t =
0.10607
= 1.04
0.10221
p-value = 0.3018
No evidence that the mean IBI values differ for the two river basins.
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10. In a test of braking performance, a tire manufacturer measured the stopping distance for one of
its tire models using 10 different vehicles. On a test track, each car made a stop from 60 miles
per hour on both wet and dry pavement. The results are contained in the file Stopping.jmp on
the course website.
Research Question – Is there evidence that on average wet pavement increases the
stopping distance of a vehicle?
Difference = Wet – Dry
H0: µd ≤ 0
Ha: µd > 0
Condition: npairs = 11 < 30 X
Reasonable to assume normal? YES
Test statistic = t =
52 - 0
11.679
=
11
52
= 14.77
3.52
p-value = 0.0001
Evidence that on average wet pavement increases the stopping distance of a
vehicle.
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