Introduction to Statistics for the Social Sciences Review for Exam 4 Homework Assignment 27

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1 Introduction to Statistics for the Social Sciences Review for Exam 4 Homework Assignment 27 Name: Lab: The purpose of this worksheet is to review the material to be represented in Exam 4. Please answer each question and we will review the solutions in class. 1. Dr. Fitzgerald works for the military designing drones (unmanned aerial vehicles) and in training pilots to fly them successfully. He is comparing four different techniques for training the drone pilots. He randomly assigned 12 student pilots to participate in one of the four training modules (3 students for each type of training). Following training they were evaluated using a flight simulator and were graded on a ten point scale. He compared the average scores for the four groups. He found no significant difference between the groups, but suspected this was due to his small sample size. He then expanded his study and measured 800 students using each type of training (200 people for each group). It turns out that while the means stayed the same, his conclusions were different. What is the most likely effect of this dramatic increase in sample size (from 3 per group to 200 per group?) 2. What will happen to variability? Variability will and so the curves will get (wider or narrower) Will it be easier or harder to reject the null? Which analysis would be most appropriate for Dr. Fitzgerald to use (e.g. chi-square, ANOVA, t-test etc)? _ A distribution has a mean of 40 and a standard deviation of 5. Find the percentile rank for a score of The 4-minute mile club is made up of 100 people, all of whom run the mile in exactly 4 minutes (neither faster nor slower, but exactly 4 minutes). The mean time for this group is 4 minutes, and the standard deviation is 4. What level of measurement is temperature (measured in degrees Fahrenheit)? Which type of study can provides evidence for a cause and effect relationship between variables, so that we can use the data to argue that changes in one variable will cause changes in another variable? Education Age IQ Income Education p =.11 p = 0.22 p = 0.02 Age p =.11 p =.91 p =.11 IQ p = 0.22 p =.91 p =.31 Income p = 0.02 p =.11 p =.31 Consider the correlations presented on this matrix and complete these statements. The relationship between & would allow you the most accurate predictions because this relationship 7. Would this be a statistically significant relationship if alpha were set at 0.05? 8. Would this be a statistically significant relationship if alpha were set at 0.01? 9. The relationship between & would allow you the weakest predictions. The p value for this correlation is. If alpha were set at 0.05 would this be a significant relationship? 10. Please refer to the matrix above, which correlations are significant at alpha = 0.05? Please refer to the matrix above, how many correlations are significant at alpha = 0.01? 11. "The proportion of the total variance in one variable that is accounted for by its relationship with the other variable" defines _

2 12. When completing a regression analysis, would the regression equation or the standard error of the estimate be the best measure of the strength of the relationship between X and Y (or the measure of how good we are at predicting Y from X)? And why? Because 13. If the correlation coefficient 0.90, what percent of variation is accounted for by the independent variable? 14. If the correlation coefficient 0.90, what percent of variation is not accounted for by the independent variable? _ 15. Marcella was interested in the relationship between the heights of mothers and the heights of their daughters. She measured 30 moms and 30 daughters. She found an observed r of.60, and a critical r of.361. How would you report this finding (alpha = 0.05)? Complete the summary for this correlation 16. According to Marcella s study what proportion of the variance of the mothers height can be accounted for by the daughters heights? And proportion of the variance of the mothers height that cannot be accounted for by the daughters heights? 17. If the correlation coefficient 0.50, what percent of variation is not explained by the independent variable? 18. Wesley is a music teacher. His pay comes from private lessons, group lessons, and for helping behind the counter in the shop. He wants to know if there is any way to predict his weekly pay based on the number of hours worked. So he completed the following regression. (See figure to right.) The coefficient of correlation is The coefficient of determination is The coefficient of regression is The proportion of variance accounted for is The proportion of variance not accounted for is The slope is The y intercept is For every additional hour that Wesley works, his pay should go up $ The difference between his predicted pay and actual pay is called a The coefficient of correlation is represented by the letter The coefficient of determination is represented by the letter The coefficient of regression is represented by the letter The proportion of variance accounted for is represented by the letter The slope is represented by the letter The y intercept is represented by the letter The coefficient of correlation can vary from what number to what number? The coefficient of determination can vary from what number to what number? The coefficient of regression can vary from what number to what number? The r 2 can vary from what number to what number? The slope can vary from what number to what number? The y intercept can vary from what number to what number? The standard error of estimate can vary from what number to what number? 19. What is the residual, and how is it similar to a deviation score? Emma has a residual score of 10 for the number of items sold. Is she over-performing or under-performing relative to her expected sales? What is the standard error of estimate, and how is it similar to standard deviation of the sample? If a scatterplot shows a perfect correlation, so that all of the dots fall on a straight line, then what is the standard error of estimate? 20. Emilio conducted an experiment to see which age group spent more money on cruise vacations; traditionalists (born ), baby boomers (born ), generation x (born ), millennial generation (born ), and the digital generation (born after 2003). He set his alpha at 0.05 and compared these five means by completing a one-way ANOVA. He calculated an observed F ratio of.02 (please notice this is an F value not a p value). What can he conclude from this analysis?

3 d16f_sbs_newlab11_agenda_exam4prep.doc 21. We are interested in predicting heating cost for the month of January from these three variables: Average January temperatures (measured in Fahrenheit degrees) Thickness of insulation in the attic (measured in inches) Age of the furnace (measured in years) There are dependent variables and independent variables. What was your regression coefficient for Intercept What was your regression coefficient for Temp What was your regression coefficient for Insulation What was your regression coefficient for Age of Furnace What is your regression equation Y = a + b1x1 + b2x2 + b3x3 22. Imogene is a manager who always tries to hire people who will make the best workers. She measured several variables of the current workers (including measures of niceness and harshness ). She wanted to use this information to predict each applicant s success score. She constructed the following multiple regression equation: Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) There are dependent variables and independent variables in her regression analysis? Review these as well 23. Imogene completed a t-test comparing the heights of men and women. She had a critical t of and an observed t of -2.17, what should she conclude? (is p< 0.05; should she reject null or not reject null; is it a significant difference) 24. Imogene wants to make her 99% confidence interval narrower. What are two things she can do? 1) 2) 25. When variability goes down is it harder or easier to reject a null hypothesis? 26. As variability (standard deviation) of a curve goes down, does the confidence interval get wider or narrower? 27. When you use a one-tail rather than two tailed test, is it harder or easier to reject a null hypothesis? (Assuming it is in the predicted direction) 28. Critical z scores (and critical t scores) create a border between what and what?

4 29. If we change our alpha from 0.05 to 0.01 what will that do to the probability of making a Type I Error? 30. Ellie wants to know whether the type of cartoon (violent versus non-violent cartoons) makes a difference in how aggressively kids behave on playground. She randomly assigned 50 kids to two groups. Half of the kids (25) watched violent cartoons and half (25) watched non-violent cartoons. Assume an alpha of Independent variable: _ Dependent variable: Is this a one-tail or two-tailed test? Is this a quasi or true experiment? What would the degrees of freedom be? What would the critical t score be? The null hypothesis is: _ If we reject the null we would conclude that: If we made a Type I Error we would conclude that when in fact If we made a Type II Error we would conclude that when in fact 31. What are the three propositions of the Central Limit Theorem? As sample size (n) goes up what happens? 1) 2) 3) 32. We compared test scores for the men and women enrolled in Dr. Rubio s Introductory Physics class. There were 30 men and 30 women tested. The variance for the men was 3 and the variance for the women was 4. The total degrees of freedom was. The pooled variance was. 33. We measured the price of homes in four neighborhoods. Please complete the following ANOVA table and report your findings dfbetween = dfwithin = MSbetween = MSwithin = Observed F = Critical F = 34. Please assume that a curve has a mean of 50 and a standard deviation of 4, please find percentile for score of 54 that 54 is exactly one standard deviation above the mean.) (Hint: Please notice

5 A little help: Useful z-scores from the z-table Standard Error of the Estimate ANOVA Equations F = MSbetween / MSwithin MSbetween = SSbetween / dfbetween MSwithin = SSwithin / dfwithin dfbetween = number of groups - 1 dfwithin = number of scores num of groups dftotal = number of scores - 1 z-table

6 t-table for Critical Values F-table for Critical Values