Web Calculator Exercise 4
Non-parametric tests (Chi-square tests,
Wilcoxon-rank-sum & Wilcoxon signed-ranks tests)
Note: When searching for a web
calculator for the Wilcoxon-rank-sum test, please be aware that this test is
also called the “Mann-Whitney U test”.
This test is used for Ordinal data and for an independent groups
design.
1.
A
high school counselor wants to examine whether the teenage pregnancy rate at
her school is different from the rate nationwide. She knows that the rate
nationwide is 15 %. She randomly selects 80 female students from her high
school. She finds that 9 out of 80
students are either pregnant now or have been pregnant previously.
a.
What
statistical test should be used to analyze the data?
b.
Identify
H0 and Ha for this study
c.
Conduct
the appropriate analysis
d.
Should
H0 be rejected? What should the researcher conclude?
2.
You
notice at the gym that it appears more women tend to work out together, whereas
more men tend to work out alone. To
determine whether this difference is significant, you collect data on the
workout preferences for a sample of men and women at your gym. The data follows.
|
Males |
Females |
|
|
Together |
5 |
8 |
|
Alone |
7 |
6 |
a.
What
statistical test should be used to analyze the data?
b.
Identify
H0 and Ha for this study
c.
Conduct
the appropriate analysis.
d.
Should
H0 be rejected? What should
the researcher conclude?
3.
A
researcher is interested in comparing the Christian maturity level of students
who volunteer for community service versus those who do not. The researcher
assumes that those who perform community service will have higher Christian
maturity scores. The maturity scores tend to be skewed (not normally
distributed). Higher scores indicate higher Christian maturity.
|
No Community Service |
Community Service |
|
32 |
47 |
|
40 |
48 |
|
54 |
59 |
|
13 |
72 |
|
20 |
80 |
|
26 |
55 |
a.
What
statistical test should be used to analyze these data?
b.
Is
this a one- or two- tailed test?
c.
Identify
H0 and Ha for this study
d.
Conduct
the appropriate analysis
e.
Should
H0 be rejected? What should the researcher conclude?
4.
A
researcher is interested in comparing tastiness of different kinds of cheese in
grilled cheese sandwiches. The
researcher expects that Cheddar cheese grilled sandwiches are rated tastier
than Swiss cheese grilled sandwiches. This
researcher wants to use a within-subjects design. Each participant tastes both Cheddar
and Swiss cheese grilled sandwiches. Except for the types of cheese used in the
grilled sandwiches, there is no difference between the two kinds of sandwiches.
Participants indicate the degree of tastiness on a 10-point scale and the
ratings appear in the following table. Tastiness scores tend to be skewed.
|
Participant |
Cheddar |
Swiss |
|
1 |
7 |
4 |
|
2 |
6 |
5 |
|
3 |
9 |
6 |
|
4 |
10 |
8 |
|
5 |
6 |
7 |
|
6 |
7 |
6 |
|
7 |
8 |
9 |
a.
What statistical test should be used to
analyze these data?
b.
Identify
H0 and Ha for this study.
c.
Conduct
the appropriate analysis.
d.
Should
H0 be rejected? What should the researcher conclude?
