# Statistics Problem Set: Independent and Dependent Variables

1. The Chicago Tribune of July 21, 1995 reported on a study by a fourth-grade student named Beth Peres. In the process of collecting evidence in support of her campaign for a higher allowance, she polled her classmates on what they received as an allowance. She was surprised to discover that the 11 girls who responded reported an average allowance of $2.63 per week, while the 7 boys reported an average of $3.18, 21% more than for the girls. At the same time boys had to do fewer chores to earn their allowance than did girls. The story had a considerable national prominence and raised the question of whether the income disparity for adult women relative to adult men may actually have its start very early in life.

a. What are the dependent and independent variables in this study? How are they measured?

b. What kind of a sampling method are we dealing with here?

c. How could the characteristics of the sample influence the results she obtained?

d. How might Beth go about "random sampling?" How would she go about "random assignment?"

e. If random assignment is not possible in this study, does that have negative implications for the validity of the study?

f. What are some of the variables that might influence the outcome of this study separate from any true population differences between boys' and girls' income?

g. Distinguish clearly between the descriptive and inferential statistical features of this example.

2. We have sent out everyone in a large introductory course to check whether people use seat belts. Each student has been told to look at 100 cars and count the number of people wearing seat belts. The number found by any given student is considered that student's score. The mean score for the class is 44, with a standard deviation of 7. Assume that the counts are normally distributed. A student who has done very little work all year has reported fining 62 seat belt users out of 100. Do we have reason to suspect that the student just made up a number rather than actually counting? (Hint: Calculate the standard score, z, of this raw score, z = (X - M)/SD = (62 - 44) / 7 = 2.57, and interpret what the z score means.)

3. A researcher analyzed the results of an experiment and found that the obtained t-value (on a t-test of independent means) was 1.29, with a total of 25 children in group 1 and 30 children in group 2. Use the table of critical values and discuss whether the null hypothesis can or cannot be rejected.

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#### Solution Preview

1. a. The independent variables in the study are Beth Peres' classmates. They are measured at nominal level (male versus female)

Dependent variable is the allowance they have and it is measured in interval variable.

b. The author used convenience sampling method.

c. Because the samples are closely related to the author and limited in her classmates, it will impact ...

#### Solution Summary

The independent and dependent variables are examined. The sampling methods characteristics are provided.