B. ANALYZING DATA FROM A COURSE'S GRADE BOOK

Problem

At the end of the semester, an "Introduction to Statistics" instructor wanted to gain insight into his students' performance by analyzing gradebook data (gradebook.sav). The instructor taught 3 large lecture sections offered at different times during the day. Since each section, depending on the time it was taught, attracted different types of students (in terms of major, age, full-time/part-time, etc.) the instructor chose a random sample of 35 students from each section to insure proper representation.

Variables

Midterm1: Student's score on the first midterm (0-100 scale)

Midterm2: Student's score on the second midterm (0-100 scale)

Diff.Mid: The difference between the two midterm exam scores (midterm1 - midterm2)

Extra credit: Did the student turn in the extra credit assignment? (0=NO, 1=YES)

Final: Student's score on the final (0-100 scale)

Class: Student's class (1=Freshman, 2=Sophomore, 3=Junior, 4=Senior)

Questions

Q1. Do the data provide evidence that the students who did not do the extra credit assignment (group 1) performed significantly worse on the final than those who did (group 2)?

Q2. The material covered by the second midterm is harder than the material covered in the first. Is this reflected by the students' grades?

Question 1

a.Before analyzing the data and discovering how performance on the final is related to whether or not the student did the extra credit, try to predict what the data will show (use your own experience and intuition).

Answers:

In this step, we choose and conduct the analyses that are needed in order to address the current question.

Before choosing the appropriate analyses, it is helpful to: Identify the relevant variables:

b.Which variable(s) among those listed below is/are particularly relevant to the current question?

oFinal

oExtra credit

oMidterm1

oMidterm2

oDiff.Mid

oClass

Answer:

c.The variable Extra credit is the ___________ variable, and is _____________.

oExplanatory; Categorical (qualitative)

oResponse; Continuous (quantitative)

Answer:

Now that we have identified and classified the relevant variable(s), we use exploratory data analysis methods to help us make important features of the data visible.

d.A meaningful display is:

oSide-by-side boxplots

oScatterplot

oTwo-way table

oPiechart

oHistogram

Answer:

e.A meaningful numerical summary to supplement the above display is

oDescriptive statistics

oCorrelation r (if appropriate)

oConditional percentages

oGroup (categorical) percentages

Answer:

f.Using this display and numerical summary, I will

oDescribe the features of a single quantitative distribution

oDescribe the features of a single categorical distribution

oCompare the distribution of a quantitative variable across several groups

oDescribe the relationship between two quantitative variables

oExamine the relationship between two categorical variables

Answer:

g.Remember, using the display and numerical summary, you need to compare the distribution of a quantitative variable across several groups. Do that by describing the key features of the display and by supporting your description with numerical measures.

Answer:

Now that we have made the important features of the data visible using exploratory data analysis, we move on to assessing the strength of evidence provided by the data using formal statistical tests.

h.The formal analysis part for the current question will focus on ______________.

oExploring the population mean

oExploring the population proportion

oComparing two population means

oExploring the mean of differences

oComparing two population proportions

oComparing more than two means

oExamining the relationship between two categorical variables

oExamining the relationship between two quantitative variables

Answer:

i.The appropriate statistical test is _____________________.

oOne sample z-test for the mean

oOne sample t-test for the mean

oOne sample z-test for the proportion

oTwo sample t-test for two means

oTwo sample z-test for two proportions

oChi-square test for independence

oANOVA F test

oRegression t-test for the slope

Answer:

j.Null hypotheses -H₀ :_____________________.

Answer:

k.Alternative hypotheses -H_a :_____________________.

Answer:

l.State the p-value of the test:

Answer:

m.What do the results you got indicate about the differences in performance on the final between students who turned in the extra credit and those who didn't?

Answer:

n.Do the data provide evidence that doing the extra credit assignment is the cause for students doing better on the final? Explain your answer.

Answer:

Question 2

o.Before analyzing the data and discovering whether indeed students generally did better on the first midterm, try to predict what the data will show (use your own experience and intuition).

Answers:

In this step, we choose and conduct the analyses that are needed in order to address the current question.

Before choosing the appropriate analyses, it is helpful to: Identify the relevant variables:

p.Which variable(s) among those listed below is/are particularly relevant to the current question?

oFinal

oExtra credit

oMidterm1

oMidterm2

oDiff.Mid

oClass

Answer:

q.The variable is the ___________ variable.

oCategorical (qualitative)

oContinuous (quantitative)

Answer:

Now that we have identified and classified the relevant variable(s), we use exploratory data analysis methods to help us make important features of the data visible.

r.A meaningful display is:

oSide-by-side boxplots

oScatterplot

oTwo-way table

oPiechart

oHistogram

Answer:

s.A meaningful numerical summary to supplement the above display is

oDescriptive statistics

oCorrelation r (if appropriate)

oConditional percentages

oGroup (categorical) percentages

Answer:

t.Using this display and numerical summary, I will

oDescribe the features of a single quantitative distribution

oDescribe the features of a single categorical distribution

oCompare the distribution of a quantitative variable across several groups

oDescribe the relationship between two quantitative variables

oExamine the relationship between two categorical variables

Answer:

u.Remember, using the display and numerical summary, you need to compare the distribution of a quantitative variable across several groups. Do that by describing the key features of the display and by supporting your description with numerical measures.

Answer:

Now that we have made the important features of the data visible using exploratory data analysis, we move on to assessing the strength of evidence provided by the data using formal statistical tests.

v.The formal analysis part for the current question will focus on ______________.

oExploring the population mean

oExploring the population proportion

oComparing two population means

oExploring the mean of differences

oComparing two population proportions

oComparing more than two means

oExamining the relationship between two categorical variables

oExamining the relationship between two quantitative variables

Answer:

w.The appropriate statistical test is _____________________.

oOne sample z-test for the mean

oOne sample t-test for the mean

oOne sample z-test for the proportion

oTwo sample t-test for two means

oTwo sample z-test for two proportions

oPaired t-test for _difference

oChi-square test for independence

oANOVA F test

oRegression t-test for the slope

Answer:

x.Null hypotheses -H₀ :_____________________.

Answer:

y.Alternative hypotheses -H_a :_____________________.

Answer:

z.State the p-value of the test:

Answer:

aa.According to the results you got, is the fact that the material covered by the second midterm is harder than the material covered by the first reflected by students' grades?

Answer: