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Statistics Homework Exam Preparation
Asked
Modified
Viewed
26
Instructions: Answer all questions and show calculations where necessary. Type answers into this Word doc and email your completed exam to me by 8pm. Please shrink graphs. Good luck.
Part 1. Short Answer (type answers into this document).
1. Why is the standard normal table found in the back jacket of nearly every statistics book in print? How does the standard normal distribution compare with a “normal distribution”? (5 pts.)
Because It is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, and it accurately describes the distribution of values for many natural phenomena.
All normal distributions, like the standard normal distribution, are unimodal and symmetrically distributed with a bellshaped curve. However, a normal distribution can take on any value as its mean and standard deviation. In the standard normal distribution, the mean and standard deviation are always fixed
2. Explain this: X⁓N(20, 6). (5 points)
3. What is the usefulness of the Empirical Rule? (5 pts.)
Empirical Rule: “68–95–99.7”
• 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean
o Most data (68%) fall within 1 standard deviation from the mean.
o Around 95% of values are within 2 standard deviations of the mean.
o Around 99.7% of values are within 3 standard deviations of the mean
4. The weight of West Virginia males is normally distributed with a mean of 196 pounds. Twentyfive percent of males weigh less than 174 pounds. Find the standard deviation. (5 points) hint: Z = (X*Xbar / s).
5. How can we use the notion of “degrees of freedom” in everyday life? (5 points)
One way is that degrees of freedom can describe business situations where management must make a decision that dictates the outcome of another variable.
Part 2. Computation
6. An airline examined jumbojet passengers to see if age was associated with seat choice. Fillin the crosstabs below. (25 pts.)
a. Complete the crosstabs table. Label fully.
First Class
Business Class
Coach Class
Seniors (65+)
12
56
144
Adults (1865)
15
61
181
Kids (117)
3
15
45
b. Find P(senior); find P(kid)
c. Find P(Bus Class and kid); find P(Coach class and Adult)
d. Find P(SeniorCoach); Find P(CoachSenior)
e. Are airline seats nominal, ordinal, interval or ratio level data? Explain in one sentence.
f. Put this table in Minitab and test the hypothesis that age is related to seat choice. Make sure to state the null and alternative hypotheses.
7. Open the attached Excel spreadsheet and paste the data into Minitab.
(25 points)
Light bulb burn times may follow a normal distribution. Find data in the column “Burn Hours.”
a. Find the mean and standard deviation of this sample.
b. Put the burn hours histogram here _____. Explain whether or not it’s a normal distribution. How did you make your determination?
c. Find the cutoff (in hrs.) for the lower quarter of light bulb burn times.
d. Find the range for the middle 50% of burn times.
e. Find the cutoff for the lowest 15% of burn times.
8. Interpreting the standard normal distribution. (12 points)
This order does not have tags, yet.
Additional Instructions
Exam 2 MPA 625—Statistics Name:__________________
March, 2023 Instructor: Dr. Mark Wilson
Note: you can use your book and notes. Do not contact anybody in class during the test period.
Instructions: Answer all questions and show calculations where necessary. Type answers into this Word doc and email your completed exam to me by 8pm. Please shrink graphs. Good luck.
Part 1. Short Answer (type answers into this document).
1. Why is the standard normal table found in the back jacket of nearly every statistics book in print? How does the standard normal distribution compare with a “normal distribution”? (5 pts.)
2. Explain this: X⁓N(20, 6). (5 points)
3. What is the usefulness of the Empirical Rule? (5 pts.)
4. The weight of West Virginia males is normally distributed with a mean of 196 pounds. Twentyfive percent of males weigh less than 174 pounds. Find the standard deviation. (5 points) hint: Z = (X*Xbar / s).
5. How can we use the notion of “degrees of freedom” in everyday life? (5 points)
Part 2. Computation
6. An airline examined jumbojet passengers to see if age was associated with seat choice. Fillin the crosstabs below. (25 pts.)
a. Complete the crosstabs table. Label fully.
First Class
Business Class
Coach Class
Seniors (65+)
12
56
144
Adults (1865)
15
61
181
Kids (117)
3
15
45
b. Find P(senior); find P(kid)
c. Find P(Bus Class and kid); find P(Coach class and Adult)
d. Find P(SeniorCoach); Find P(CoachSenior)
e. Are airline seats nominal, ordinal, interval or ratio level data? Explain in one sentence.
f. Put this table in Minitab and test the hypothesis that age is related to seat choice. Make sure to state the null and alternative hypotheses.
7. Open the attached Excel spreadsheet and paste the data into Minitab.
(25 points)
Light bulb burn times may follow a normal distribution. Find data in the column “Burn Hours.”
a. Find the mean and standard deviation of this sample.
b. Put the burn hours histogram here _____. Explain whether or not it’s a normal distribution. How did you make your determination?
c. Find the cutoff (in hrs.) for the lower quarter of light bulb burn times.
d. Find the range for the middle 50% of burn times.
e. Find the cutoff for the lowest 15% of burn times.
8. Interpreting the standard normal distribution. (12 points)
Calculate the area left of 1.1.
Calculate the area from 0.6 to 1.8.
Use the Empirical Rule to estimate the area to the left of 1 added to the area to the right of 2.
1
1
Exam 2
MPA 625
—
Statistics
Name:__________________
M
arch
, 202
3
Instructor: Dr. Mark Wilson
N
ote
:
you can use your book and notes.
D
o not contact anybody in class during the
test period.
Instructions: Answer all questions
and s
how calculation
s
where necessary.
Type
answers into this Word doc and e
mail your completed exam to me by
8pm
.
Please
shrink graphs.
Good
luck.
Part 1. Short Answer
(type
answers into this document).
1.
W
hy is the standard normal table found in the back jacket of nearly every
statistics book in print
?
How does the standard normal distribution compare with
a “normal distribution”?
(
5
pts.)
2.
Explain this: X
?
N(
2
0, 6
).
(5
points)
3.
W
hat is the usefulness
of
the
E
mpirical
R
ule
?
(
5
pts.)
4.
The weight of West Virginia males is normal
ly distributed with a mean of 19
6
pounds. T
wenty

five percent of
males weigh less than 1
74
pounds.
Find
the
s
tandard
deviation
.
(5
points)
h
int
:
Z
=
(
X
*

X
bar / s
)
.
5.
H
ow can we use the notion of
“
degrees of freedom
”
in
every
day life
? (
5
points)
1
Exam 2 MPA 625—Statistics Name:__________________
March, 2023 Instructor: Dr. Mark Wilson
Note: you can use your book and notes. Do not contact anybody in class during the
test period.
Instructions: Answer all questions and show calculations where necessary. Type
answers into this Word doc and email your completed exam to me by 8pm. Please
shrink graphs. Good luck.
Part 1. Short Answer (type answers into this document).
1. Why is the standard normal table found in the back jacket of nearly every
statistics book in print? How does the standard normal distribution compare with
a “normal distribution”? (5 pts.)
2. Explain this: X?N(20, 6). (5 points)
3. What is the usefulness of the Empirical Rule? (5 pts.)
4. The weight of West Virginia males is normally distributed with a mean of 196
pounds. Twentyfive percent of males weigh less than 174 pounds. Find the
standard deviation. (5 points) hint: Z = (X*Xbar / s).
5. How can we use the notion of “degrees of freedom” in everyday life? (5 points)
Sheet1
Hours Measures the time 60W bulbs burn until failure
1215.79
1071.83
1231.25
1224.03
1145.04
1237.43
1141.86
1352.61
1044.33
1234.77
1114.9
1356.04
1256.22
1295.33
1243.79
1255.62
1263.61
1327.04
1370.65
1177.6
1130.55
1335.57
1160.07
1257.08
1329.73
1286.74
1155.73
1070.7
1271.07
1155.32
1273.69
1317.31
1150.15
1208.5
1314.87
1282.07
1276.57
1229.51
1300.3
1177.32
1160.95
1093.36
1135.16
1359.03
1184.25
1123.07
1319.46
1208.55
1149.76
1355.47
1240.46
1282.83
1223.81
1248.94
1267.17
1256
1341.08
1510.35
1256.53
1262.41
1187.32
1342.02
1346.65
1422.32
1166.29
1356.84
1235.8
1413.94
1244.2
1286.64
1130.44
1281.16
1247.88
1291.82
1225.07
1214.48
1227.56
1295.73
1296.05
1287.07
1210.13
1262.04
1238.68
1240.36
1358.89
1201.33
1319.96
1330.31
1200.4
1274.12
1255.55
1243.11
1267.78
1151.56
1203.85
1239.09
1263.95
1459.85
1108.45
1250.5
1215.79
1071.83
1231.25
1224.03
1145.04
1239.43
1181.86
1352.61
1044.33
1234.77
1111.49
1336.04
1256.22
1295.33
1243.79
1255.62
1270.61
1327.04
1340.65
1177.6
1130.55
1350.57
1170.07
1257.08
1329.73
1286.74
1155.73
1075.7
1271.07
1155.32
1273.69
1317.31
1150.15
1204.5
1314.87
1282.07
1276.57
1229.51
1310.3
1177.32
1160.95
1093.36
1135.16
1379.03
1184.25
1123.07
1319.46
1208.55
1169.76
1335.47
1240.46
1242.83
1223.81
1248.94
1267.17
1296
1341.08
1510.35
1256.53
1265.41
1187.32
1342.02
1336.65
1422.32
1176.29
1356.84
1235.8
1413.94
1240.2
1286.64
1130.44
1281.16
1247.88
1299.82
1225.07
1214.48
1227.56
1295.73
1296.05
1280.07
1210.13
1262.04
1238.68
1240.36
1358.89
1201.33
1319.96
1330.31
1220.4
1274.12
1255.55
1243.11
1267.78
1151.56
1203.85
1239.09
1263.95
1459.85
1108.45
1257.5
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