Reference no: EM132851116

A small random sample (n=4) was drawn from each of two populations: females in a statistics class at CSUN, and males in a statistics class at CSUN. The variable measured was the number of hours individuals in each of these samples worked while in school, and you are interested in estimating the differences between the populations from which these samples were drawn, to see if there is an effect of gender on hours worked. Here are the numbers of hours per week indicated by each of the 4 participants in each sample:

12 0 35 30

17 32 0 12

1. What is the independent variable? What is the dependent variable?
2. Calculate the mean of each sample.
3. Which index of standard deviation (i.e. s, s-hat, or sigma) should be used if we are calculating the variability in each of these samples in order to estimate the population (the entire class) variability?
4. Calculate the standard deviation (remember, you decided it should be s, s-hat, or sigma above!) of Females using the deviation score formula.
5. Calculate the standard deviation (remember, you decided it should be s, s-hat, or sigma above!) of Males using the raw score formula.
6. Interpret your findings - what do the means tell you about the two groups?
7. What do the standard deviations tell you about the two groups?
8. Calculate the effect size "d" for the difference between the two sample means, using the pooled/average standard deviation = 14.72 in the formula.
9. What size is this effect?
10. Two new (fictional) students have joined the statistics class at CSUN. Their counselors are concerned about their ability to concentrate on their coursework, but for different reasons. Mike's counselor is concerned because he works 30 hours per week, while Matt's counselor is concerned because he spends 6 hours per week at parties and bars. Based on the typical amounts of time that the other students in the statistics class spend doing these things, which student should we be more concerned about? That is, which student's activities are more outside what is acceptable for the majority of students? The mean number of weekly hours worked by students in our class is 18.56, with a standard deviation of 16.14. The mean number of weekly hours spent by students at parties and bars is 2.18, with a standard deviation of 2.54. Use Z scores to determine which student has the more extreme amount of time spent on non-coursework activities.
11. Why do we need to use Z scores to make this determination? Why can't we just compare the raw scores of 30 hours per week worked and 6 hours per week at parties, and see which number is larger?