Answer the following questions:

1. Define inferential statistics and how researchers use inferential statistics to draw conclusions from sample data.

2. Define probability and discuss how it relates to the concept of statistical significance.

3. A researcher is studying the effects of yoga on depression. Participants are randomly assigned to one of two groups: yoga and medication (experimental group); or support group and medication (control group). What is the null hypothesis? What is the research hypothesis?

4. In the scenario described in the previous question, the researcher implements two programs simultaneously: a 6-week yoga program coupled with medication management and a 6-week support group program coupled with medication management. At the end of the 6 weeks, participants complete a questionnaire measuring depression. The researcher compares the mean score of the experimental group with the mean score of the control group. What statistical test would be most appropriate for this purpose and why? What is the role of probability in this statistical test?

5. In the scenario described in the previous questions, the researcher predicted that participants in the experimental group-yoga plus medication-would score significantly lower on measures of depression than would participants in the control group-support group plus medication. True or false: A two-tailed test of significance is most appropriate in this case. Explain your response.

6. Explain the relationship between the alpha level (or significance level) and Type I error. What is a Type II error? How are Type I and Type II errors different?

7. A researcher is studying the effects of sex-male and female-and dietary sugar on energy level. Male and female participants agree to follow either a high sugar or low sugar diet for eight weeks. The researcher asks the participants to complete a number of questionnaires, including one assessing energy level, before and after the program. The researcher is interested in determining whether a high or low sugar diet affects reported energy levels differently for men and women. At the end of the program, the researcher examines scores on the energy level scale for the following groups: Men - low sugar diet; Men - high sugar diet; Women - low sugar diet; Women - high sugar diet. What statistic could the researcher use to assess the data? What criteria did you use to determine the appropriate statistical test?