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# Application of Non-Parametric Tests

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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?