a) A researcher wants to assess if there is a relationship between the concentration of fluoride in drinking water and the number of cavities in children's teeth (data is normally distributed).

b) A researcher wants to assess if physical activity alleviates depression. Sixty participants are randomly allocated to one of three groups: no exercise; 20 minutes of jogging per day; or 60 minutes of jogging per day. At the end of a month, the researcher asks each participant to rate how depressed they now feel, on a Likert scale that runs from 1 ("totally miserable") through to 100 (ecstatically happy").

c) A researcher wants to assess the effect of using different modalities for 10 days to gain a pain-free range of motion (ROM) in patients with elbow tendonitis. Four groups are created and four modalities of care are offered. One gets ultrasound; another one gets ice; a third one gets a massage, and the fourth is assigned to be the control. The dependent variable is elbow ROM, measured in degrees and is normally distributed; the independent variable (the type of modality) has four levels.

d) A researcher is interested in identifying how the relationship between the blood pressure levels of newborns and infants relate to subsequent adult blood pressure. The researchers found that the blood pressure of a newborn is affected by several extraneous factors such as birthweight and the day of life on which blood pressure is measured. In this study, the infants were weighted at the time of the blood-pressure measurements. The researchers referred to this weight as the "birth weight", although it differs somewhat from the actual weight at birth. Because the infants grow in the first few days of life, the researchers expected that infants seen at 5 days of life would on average have a greater weight than those seen at 2 days of life. The dependent variable was systolic blood pressure and the independent variables were birthweight and age in days.

e) An investigator is interested in predicting cholesterol level (dependent variable) using body weight as the independent variable). The researcher believes that blood pressure, gender, age, and diet may be potential confounders

f) After finding that there is a correlation between birth weight (dependent variable) and gestational age (independent variable), a researcher wants to investigate how birthweight depends on gestational age.

g) A researcher wants to assess whether attitudes towards pay discrimination ( attitudes are measured on an ordinal scale from "strongly agree" to "strongly disagree",) differed based on job position: (assistant professor; associate professor and full professor). It is assumed that the data is not normally distributed.

h) A researcher wants to assess the correlation between two variables. One or both of the variables are not assumed to be normally distributed, and least one of them is ordinal.

i) A researcher wants to assess the correlation between two continuous normally distributed variables: heart rate and level of exertion

j) A researcher has a study with a categorical independent variable (with two or more categories) and a normally distributed interval dependent variable; he wishes to test for differences in the means of the dependent variable broken down by the levels of the independent variable.