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# STAT 40001/STAT 50001 Homework 2 solved

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Q.N. 1) Table 1 and Table 2 below are the test scores of 10 students in Test 1 and Test 2 in addition to
their major field of study and class standing
Name Major Test 1
Ana MA 56
Brian MA 78
Cathy CS 87
Dough CS 89
John STAT 95

Lucas STAT 98
Marcus STAT 59
Nabin MA 78
William CS 87
Zoe STAT 98
Table 1: Test 1 Scores
Name Class Test 2

Ana Junior 86
Brian Junior 67
Cathy Senior 78
Dough Junior 89
John Senior 87
Lucas Senior 67
Marcus Junior 94

Nabin Senior 78
William Senior 81
Zoe Junior 83
Table 2: Test 2 scores
a) Use merge(.,.) to create a single table containing the student’s test 1 and test 2 scores.
b) How many students did better in the second test?
c) How many students did better in the first test?
d) How many students have the same score in both tests?
e) Calculate the average and standard deviation of both tests.
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Q.N. 2) The dataset related to health insurance customers is provided in custdata.tsv. Here, “tsv”stands
for tab-separated values.
a) Import the data in R
b) Display the age distributions of the customers using a histogram.
c) Display the marital status of all the customers using bar graph.
d) How many customers are from the state of Indiana?

Q.N. 3) Access the data from url http://www.stat.berkeley.edu/users/statlabs/data/vote.data
and store the information in an object named vote using the function read.table(). This includes the 1988
Stockton Primary Exit Poll Survey:
a) How many variables are included in the survey? Please print the variables.
b) One of the variable included is the voter’s race. Note that following code are used.
0 = missing, 1 = W hite, 2 = Hispanic, 3 = Black, 4 = Asian, 5 = Other
Display the distribution of the voter’s race graphically.

Q.N. 4) This dataset (YouthRisk, provided with this assignment) is derived from the 2007 Youth Risk
Behavior Surveillance System (YRBSS), which is an annual survey conducted by the Centers for Disease
Control and Prevention (CDC) to monitor the prevalence of health-risk youth behaviors. This dataset focuses on whether or not youths have recently (in past 30 days) ridden with a drunk driver. The description
of the variables is provided at
https://vincentarelbundock.github.io/Rdatasets/doc/Stat2Data/YouthRisk.html
a) Import the data in R and determine its dimension.

b) Is there any missing value? If so please remove the missing values from the data set.
c) Display the age distribution of the individuals based on gender using Parallel boxplot.
d) Display the grade(Year in high school) distribution using a pie chart.

Q.N. 5) Generate 500 random numbers from normal distribution with mean 10 and variance 25. How
many observations are within one, two and there standard deviations from the mean? Compare your
findings with the empirical rule.
According to the empirical rule 68%, 95% and 99.7% data reside within one, two and three standard
deviation of the mean. Does your data meet this rule?

Q.N. 6) FEV (forced expiratory volume) is an index of pulmonary function that measures the volume
of air expelled after one second of constant effort. The data provided in the link below contains determinations of FEV on children ages 6-22 who were seen in the Childhood Respiratory Disease Study in 1980
in East Boston, Massachusetts. The data are part of a larger study to follow the change in pulmonary
function over time in children.
ID – ID number
Age – years FEV – litres
Height – inches

Sex – Male or Female
http://www.statsci.org/data/general/fev.txt
a) Import the data in R. How many children are included in this study?
b) Display the FEV of Male and Female children.
c) Test the hypothesis whether there is a difference in FEV for male and female.
d) Construct a 95% confidence interval for the difference in the mean FEV for male and female students.
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Q.N. 7) The employee satisfaction in any job depends on several factors including the salary. The attached data (Employee Satisfaction) provides information about 15000 employees.
a) Import the data in R
b) Display the satisfaction scores for low, medium and high salary employees.
c) Test whether the job satisfaction level for high earning employees is significantly different from the low
earning employees.

Q.N. 8) Results from an experiment to compare yields (as measured by dried weight of plants) obtained
under a control and two different treatment conditions is provided in the data frame PlantGrowth in the
R dataset.
a) How many observations are recorded in the data set?
b) What is the mean of each of the control and treatment conditions?
c) Test the hypothesis whether there is a significance difference between the treatment 1 and treatment 2.

Q.N. 9) The babies data frame in the UsingR packages has a collection of variables taken for each new
mother in a Child and Health Development Study. The variable age contains the mom’s age and the
variable dage contains the dad’s age for several babies. Do a significance test of the null hypothesis of
equal ages against a one-sided alternative that dads are older.

Q.N. 10) A person makes a doctor appointment, receives all the instructions and doesn’t show up for
appointment, Who to blame? Data set containing some information including the age, gender are provided
in the data set (Noshow). (Other variable names are self-explanatory).
a) Import the data in R and identify its dimension
b) Print the variables included in the dataset.

c) Display the Age distribution by gender creating parallel box plot.
d) Test whether female are more likely to miss the appointment than male.
e) Are female older than male? Perform the test.
(Hint: xtabs function in R will be useful to create Cross-Tabulation in part(d))
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