Please Read All Questions Carefully And Make Sure You Answer

Please read all questions carefully, and make sure you answer all parts

Please read all questions carefully, and make sure you answer all parts. Give reasons for your answers where required. Answers without explanation will not receive credit.

1. The frequency distribution for a sample of observations on a variable X is represented by the histogram below. For the interval with a midpoint of 50, write (1) the frequency; (2) the relative frequency, given 80 observations in all.

2. In the distribution above, which of the following is the most likely value for the mean? Explain your answer (use the space beside and below the options): (A) 29, (B) 35, (C) 41, (D) . In the distribution shown in Question 1, which of the following is the most likely value for the standard deviation? Explain your answer, including reasons for rejecting EACH alternative: (A) -12, (B) 6, (C) 12, (D) .

3. If the mean is less than the median, what does it indicate? Check TRUE (T) or FALSE (F) for each statement below. None or more than one may be true. (A) The distribution is negatively skewed. T F (B) The calculations for the median are incorrect. T F (C) The median is being pulled upward by extreme values. T F (D) More than half the observations are above the mean. T F

4. Determine whether EACH of the following statements about the standard deviation is true or false. More than one statement may be true. (Circle T for True or F for False.) (A) It cannot be computed when the distribution is skewed. T F (B) It is unaffected by adding a constant to every score. T F (C) It increases as the number of observations increases. T F (D) A small standard deviation means that the variable is accurately measured. T F

5. For the variables below, determine which measure of central tendency would be most appropriate. Give reasons for your choices. (a) Sport played (football, basketball, baseball, etc.) by professional athlete in a survey of professional athletes’ attitudes about their responsibilities as role models. (b) Income of all employees of a large corporation. (c) Consumer ratings of product quality on a 5-point scale (1 = unacceptable; 5 = excellent) based on a sample of 50 consumers. (d) Score on a Reading achievement test.

6. In a study of variables related to antisocial behavior in adolescents, 50 teenage boys and 46 teenage girls were administered various personality and behavioral scales along with a measure of propensity for antisocial behavior (PASB) (higher score means greater propensity for antisocial behavior). Box-and-whiskers plots of the distributions for the boys and girls on the PASB scale are shown below. Evaluate EACH of the following statements and decide whether it is true or false for these data. Check TRUE or FALSE for each. Give reasons for your answers. (a) The distribution for males is negatively skewed. T F (b) 50% of the males have a PASB score between 24 and 28. T F (c) 25% of the females have a PASB score less than 22. T F (d) The median PASB score for females is the same as the 25th percentile for males. T F (e) A female with a score of 12 on the PASB scale would be considered an outlier. T F

7. In the distribution in question 7, the overall mean and standard deviation were 27 and 6, respectively. Students’ scores were converted to z-scores for greater interpretability. (a) If a student was half a standard deviation above the mean on the PASB scale, what would the student’s z-score be? Explain your answer. (b) A certain student had a z-score of 1.25 on the PASB. What was the student’s score on the original PASB scale? Show how you obtained your answer. (c) Suppose that to avoid negative scores, the z-scores were re-scaled by multiplying each score by 10 and adding 100. What would the mean and standard deviation of the new set of scores be? Mean = SD = 9. In the study described in Question 7, the researcher also gathered data on several other variables, including scores on a measure of aggression (higher score indicates greater aggression), and scores on a self-esteem scale (higher score indicates greater self-esteem). In addition, participants were asked about their involvement in student organizations (0 = no involvement, 1 = sport-related activities only, 2 = cultural activities only; 3 = political activities only; 4 = more than one type of activity). (a) The researcher calculated Pearson correlation coefficients to assess the relationships among all the variables and found a correlation of -.5 between propensity for antisocial behavior and involvement in student organizations. The researcher concluded that teenagers who are more involved in student organizations have lower propensity for antisocial behavior. Do you agree with this conclusion? Explain. The scatterplot of PASB against Aggression for the total sample is shown below and the scatterplot of Self-esteem against PASB is shown below. (b) Determine whether each of the following statements about the relationships depicted in Figures 1 and 2 is true or false. Circle TRUE or FALSE for each. (1) Because PASB is low when Aggression is low, the correlation between these variables is negative. T F (2) The Pearson correlation coefficient is an appropriate measure of the relationship between Aggression and PASB. T F (3) Individuals with either low or high levels of PASB scores experience low self-esteem and individuals with moderate levels of PASB have higher self-esteem, so there is no relationship between these variables. T F (c) Which of the values below is the most likely value for the correlation between PASB and self-esteem (Figure 1)? Give reasons for your choice. (A) -0.6 (B) 0.0 (C) 0.5 (D) 0.9 (d) In writing up the results, the researcher struggled to draw a conclusion and debated the following three possibilities: (1) “The results of this study indicate that Aggression measures may be useful in predicting which students are likely to engage in antisocial behaviors." (2) “The results of this study suggest that a program aimed at reducing students’ propensity for antisocial behavior will likely reduce their aggression levels as well." (3) “The results of this study suggest that high levels of antisocial behavior are associated with high levels of aggression. Hence, aggression management programs should be offered in schools in order to reduce propensity for antisocial behaviors among adolescents." Which of these conclusions, if any, is valid? Explain your answer, indicating why you think EACH conclusion is valid or invalid.

8. Refer to the scatterplot of PASB against Aggression (Figure 1). A correlation of .4 between Aggression and PASB was obtained. What proportion of the variance in PASB is accounted for by Aggression?

9. What would happen to the size of the correlation between Aggression and PASB (Figure 1) if the outlier (leftmost point in the figure) were removed? (A) It would decrease. (B) It would remain the same. (C) It would increase. (D) We cannot predict what the result would be.

10. Which of the following equations is most likely to be the least squares regression line for the data in the scatterplot in Figure 1 (based on all observations)? Explain your answer. (1) 10 + .7x (2) 20 + 1.2x (3) 14 + .2x (4) 5 + .5x

11. What would be the likely effect of each of the following factors on the correlation between PASB and Aggression? Indicate DECREASE (D), INCREASE (I), or NO CHANGE (NC). Explain your answer. (1) Expanding the sample to include undergraduate college students. D I NC (Assume variability in one or both measures increases.) (2) Rescaling the PASB scores to z-scores before calculating the correlation. D I NC (3) Selecting the sample from students whose records showed incidents of anti-social behaviors at school. D I NC (4) Increasing the sample size. D I NC

12. The score interval midpoint of 97 in the distribution is associated with a frequency of 5.