Download Homework 1

STAT 5615: Statistics in Research I
Be sure to complete the quiz on Canvas to submit your answers for this homework.
Problem 1:
In a University of Wisconsin (UW) study about alcohol abuse among students, 100 of the 40,858
members of the student body in Madison were sampled and asked to complete a questionnaire. One
question asked was, “On how many days in the past week did you consume at least one alcoholic
drink?”
Use this information to answer Questions 1-5.
1. Identify the population. Select from the options below.
o Entire UW student body of 40,858 students
o All college students across the country
o 100 students who were asked to complete the questionnaire
o Alcohol abuse among University of Wisconsin students
2. Identify the sample. Select from the options below.
o Entire UW student body of 40,858 students
o All college students across the country
o 100 students who were asked to complete the questionnaire
o Alcohol abuse among University of Wisconsin students
3. For the 40,858 students at UW, one characteristic of interest was the percentage who respond
“zero” to this question. For the 100 students sampled, suppose 29% gave this response. Does
this mean that 29% of the entire population of UW students would make this response?
Select from the options below.
o Yes; As a result of random sampling, the results of the sample are the same results for
the population
o No; sample results are generalized to the population but they are not necessarily
identical
4. Is the numerical summary of 29% a sample statistic or a population parameter? Select from
the options below.
o Sample statistic
o Population parameter
5. Match the description with the correct sampling technique. The sampling technique options
are: Simple Random Sample, Cluster Random Sample, Stratified Random Sample,
Systematic Sample
o Randomly select 100 students from all the 40,858 students (e.g., put all the 40,858
names in a column of Excel spreadsheet or JMP, generate random numbers in a
column next to the name column, sort the names of students according to the
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generated random numbers, and then select the first 100 students in the randomly
sorted list of names).
o Split the entire student body by class level (freshman, sophomore, junior, senior,
graduate) and randomly sample 20 people from each class.
o Obtain a list of all 40, 858 students and select every 408th student from the list until
100 students are selected.
Problem 2:
Twenty-seven daily precipitation measurements (in inches) were measured from an unspecified
Midwestern experiment station. The data set is available below.
0.095
0.205
0.215
0.350
0.105
0.290
0.060
0.210
0.005
0.425
0.220
0.105
0.115
0.155
0.110
0.225
0.165
0.340
0.070
0.275
0.455
0.045
0.250
0.065
0.450
0.005
0.335
The data set is also available in the uploaded excel file “Problem2.csv” on Canvas.
Use this information to answer Questions
6-11.
6.
Identify the histogram from this
set of graphs.
o (A)
o (B)
o (C)
o (D)
7. Identify the box plot from this set
of graphs.
o (A)
o (B)
o (C)
o (D)
8. Using software compute the sample mean. Use 3 decimal places.
9. Using software compute the sample median. Use 3 decimal places.
10. Using software compute the sample standard deviation. Use 3 decimal places.
11. Based on the overall picture of this data from the summary statistics and graphs, select the
best summary of this data.
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o The distribution of the data is rather symmetric because of the similar length of the
whiskers in the box plot, the median falls close to the center of the box, and there
seems to be a single peak of the histogram. The similarity of the median and mean
also suggests symmetric behavior.
o The distribution of the data is highly left skewed. One whisker is much longer
compared to the other whisker in the box plot. Also the left tail of the histogram is
longer representing a left skew. The comparison of the mean and median also
suggests left skewness.
o The distribution of the data is highly right skewed. One whisker is much longer
compared to the other whisker in the box plot. Also the right tail of the histogram is
longer representing a right skew. The comparison of the mean and median also
suggests right skewness.
Problem 3:
Educational researchers study trends in SAT scores to assess claimed differences between male and
female performance on the exams. The scores were further divided into verbal and math parts. So they
have 4 types (male/verbal, female/verbal, male/math, female/math) of average SAT scores recorded for
years 1967, 1970, 1975, 1985, 1990, and 1993-1996. The data set is available in the uploaded Excel file
“Problem3.csv”.
Use this information to
answer Questions 12-13.
12. Identify the
plot of the four
separate time
series overlaid
on the same
plot.
o (A)
o (B)
o (C)
o (D)
13. Select the statement below that most accurately describes the time series plot.
o Overall the female math scores are lower than all other scores from 1967 until 1996.
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o The trends in scores from 1967-1996 between males and females have changed
dramatically.
o The male math score resulted in the largest decrease from 1970 to 1975.
Problem 4:
Because the import of basic materials is an indication of the strength of the U.S. economy, the
Commerce Department monitors the importation of steel. The following data are the level of steel
imports (in millions of tons) for the years 1985 to 1996. The data set is available in the uploaded Excel
file “Problem4.csv”.
Year
Import
Year
Import
Year
Import
1985
27.6
1990
21.9
1995
27.3
1986
22.7
1991
20.2
1996
32.1
1987
21.9
1992
21.9
1988
20.4
1993
21.8
1989
19.7
1994
32.7
Use this information to answer Question 14.
14. Construct a bar chart for the data and select ALL the statements below that are accurately
reflected in the bar chart.
o The distribution of steel imports is symmetric.
o There was a decline from the late 80’s of steel imports.
o The distribution of steel imports is right skewed.
o An abrupt surge upward occurred after 1993.
o The year 1996 saw the highest level of steel imports.
o The distribution of steel imports is left skewed.
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