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Lesson 9: Comparing Two Groups
NAME
Lab Activity
Answer the following questions showing all work. For questions
that require Minitab Express include the appropriate output (copy
+ paste) along with an explanation. For all tests use an alpha level
of .05 unless otherwise specified.
1. For each of the following scenarios, which of the following hypothesis
tests is most appropriate: one sample proportion, one sample mean,
two independent proportions, two independent means, or two paired
(dependent) means? Explain why. (30 points)
a) single mean test which is one tailed[z test]
b) two proportion test which is one tailed[z test]
c) two proportion test which is one tailed[z test]
d) two proportion test which is one tailed[z test]
e) Single proportion test which is two tailed[z test]
f) two proportion test which is one tailed[z test]
g) Two mean test which is two tailed
A. A bakery advertises that their cupcakes weigh 100 grams. A group of
customers believe that this is false advertising and that the average
weight of this bakery?s cupcakes is really less than 100 grams.
B. The physics department at one college wants to know if physics
majors? SAT-Math scores are higher than their SAT-Verbal scores. They
take a simple random sample of 30 physics majors and ask each student
for his or her SAT-Math and SAT-Verbal scores.
C. The admissions office at a liberal arts school wants to know if
applicants to their music education program have higher SAT-Verbal
scores than applicants to their elementary education program.
D. Students at Penn State and Michigan State are arguing over which
university?s students have better SAT-Writing essay scores. They take a
Lesson 9: Comparing Two Groups
NAME
Lab Activity
random sample of 50 students from each university and record their
SAT-Writing essay scores.
E. In the population of all Penn State World Campus students, 18.6%
have military experience. An instructor at Penn State Harrisburg wants
to know if the proportion of students at Penn State Harrisburg is
different from 18.6%. She takes a random sample of 100 Penn State
Harrisburg students and asks if they?ve had military experience.
F. A group of developmental psychologists are conducting a study on
male/female fraternal twins. They want to know if the female twins
tend to have higher emotional intelligence scores than their male twin
counterparts. They have a sample of 20 male/female fraternal twins
and give each an emotional intelligence test.
G. Nursing students want to compare the resting heart rates of college
students who exercise regularly and college students who do not
exercise regularly. They have a sample of 100 college students: 60 who
claim to exercise regularly and 40 do not. They measure each
individual?s resting heart rate.
H. The Department of Statistics wants to compare the proportion of men
and women who pass STAT200. They take a random sample of 500
students enrolled in STAT200 and at the end of the semester record
their gender and whether or not they passed the course.
I. A pharmaceutical company wants to compare the LDL cholesterol
levels of patients who have taken two different drugs (Drug A and Drug
B). They randomly assign 30 patients to receive Drug A and 30 patients
to receive Drug B. After taking 90 days they measure each patient?s LDL
cholesterol level.
Lesson 9: Comparing Two Groups
NAME
Lab Activity
J. A group of psychology students what to know if wives tend to have
higher marital satisfaction levels than their husbands. They have a
sample of 30 married heterosexual couples. The husband and wife each
complete a test of marital satisfaction.
Lesson 9: Comparing Two Groups
NAME
Lab Activity
2. I want to compare my students? scores on the Midterm I Practice Quiz and
the Midterm I exam. In a sample of 33 students, the mean difference was
6.159 points with a standard deviation of 15.156. Scored tended to be higher
on the practice quiz. Use Minitab / Minitab Express to answer the following
questions. You will have to enter in these statistics as ?summarized data.? (16
points)
A. Construct a 95% confidence interval for the mean difference between
the Midterm I Practice Quiz and Midterm I exam.
The obtained output is given below,
One-Sample T
Test of ? = 0 vs ? 0
N
33
Mean
6.16
StDev
15.16
SE Mean
2.64
95% CI
(0.78, 11.53)
T
2.33
P
0.026
From the above output we can see that the 95% confidence interval for the mean
difference between the Midterm I Practice Quiz and Midterm I exam is (0.78,
11.53).
B. Given the null hypothesis ?d = 0, and alternative hypothesis ?d? 0,
what is the p value?
From the output we can see that the required p-value is 0.026.
C. Is there evidence that students scored differently on the Midterm I
Practice Quiz and Midterm I? Why?
As the p-value is smaller than the significance level of 0.05 so we are rejecting the
null hypothesis and concluding that there is sufficient evidence that students
scored differently on the Midterm I Practice Quiz and Midterm I.
Lesson 9: Comparing Two Groups
NAME
Lab Activity
3. Open the SP16STUDENTDATA.MTW dataset. Assume that this is a sample
that is representative of the population of all World Campus STAT200 students.
We want to know if males and females differ in terms of what they believe is
the ideal age to get married. (22 points)
A. Write the null and alternative hypothesis using the appropriate
symbols.
B. Does this scenario require an independent samples or paired
samples t test? Why?
C. For the variable of ?ideal marriage age,? are the standard deviations
for males and females similar or different? (If one is more than twice of
the other they are different)
D. Compute the appropriate test statistic. (I strongly encourage you do
to this in Minitab/Minitab Express and NOT by hand)
E. What is the p value?
F. Is your decision to reject or fail to reject the null hypothesis from part
(A)? Why?
G. Is there statistical evidence that the ideal marriage age of males and
females is different on average?
H. How could you answer this research question using a confidence
interval? (You don?t have to actually do it, just explain what you could
do.)
Lesson 9: Comparing Two Groups
NAME
Lab Activity
4. Open the dataset SP16STUDENTDATA.MTW. Assume that this is a sample
that is representative of the population of all World Campus STAT200 students.
(32 points)
A. Construct a 95% confidence interval for the difference in the heights
of male and female students.
B. Interpret the 95% confidence interval that you constructed in part
(A).
C. Given your results from part (A), is there evidence that male and
female students differ in terms of their heights? Explain why?
D. Construct a 95% confidence interval for the difference in the
proportion of males and females who are dieting.
E. Interpret the 95% confidence interval that you constructed in part
(D).
F. Use the five-step hypothesis testing procedure to determine if there is
a difference in the proportion of Pennsylvania and non-Pennsylvania
residents who own a dog.
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
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