**File attached as well, same as below** 1. Calculate SP (the sum of products of deviations) for the following scores. X Y 3 3 4 1 0 9 2 2 1 5 2. For the following scores, compute the Pearson correlation. X Y 4 4 7 7 3 7 1 2 5 6 4 4 3. Even a very small effect can be significant if the sample is large enough. Suppose, for example, that a researcher obtains a correlation of r=0.60 for a sample of n=10 participants. a. Is this sample sufficient to conclude that a significant correlation exists in the population? Use a two-tailed test with =.05. b. If the sample had n=25 participants, is the correlation significant? Again, use a two-tailed test with =.05. 4. For the data below: a. Find the regression equation for predicting political participation from life satisfaction. b. Using =.05, test the significance of the regression equation. X Y 5 10 3 6 6 7 4 3 2 4 5. There appears to be some evidence suggestion that earlier retirement may lead to memory decline (Rohwedder & Willis, 2010). The researchers gave a memory test to men and women aged 60 to 64 years in several countries that have different retirement ages. For each country, the researchers recorded the average memory score and the percentage of individuals in the 60 to 64 age range who were retired. Note that a higher percentage retired indicates a younger retirement age for that country. The following data are similar to the results from the study. Use the data to find the regression equation for predicting memory scores from the percentage of people aged 60 to 64 who are retired. Country % Retired (X) Memory Score (Y) Sweden 39 9.3 U.S.A. 48 10.9 England 59 10.7 Germany 70 9.1 Spain 74 6.4 Netherlands 78 9.1 Italy 81 7.2 France 87 7.9 Belgium 88 8.5 Austria 91 9.0 6. A researcher is interested in consumer preferences among three brands of yogurt. A sample of 90 people is obtained, and each individual is asked to taste each brand and then select his/her favorite. The resulting frequency data are as follows: Brand A Brand B Brand C 37 21 32 Do the data indicate any significant preferences among the three brands? Test with =.05 level of significance. 7. Data from the department of motor vehicles indicate that 80% of all licensed drivers are older than age 25. a. In a sample of n=60 people who recently received speeding tickets, 38 were older than 25 years and the other 22 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use =.05. b. In a sample of n=60 people who recently received parking tickets, 43 were older than 25 years and the other 17 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use =.05. 8. Automobile insurance is much more expensive for teenage drivers than for older drivers. To justify this cost difference, insurance companies claim that the younger drivers are much more likely to be involved in costly accidents. To test this claim, a researcher obtains information about registered drivers from the department of motor vehicles (DMV) and selects a sample of n=300 accident reports from the police department. The DMV reports the percentage of registered drivers in each age category as follows: 16% are younger than age 20; 28% are 20 to 29 years old; and 56% are age 30 or older. The number of accident reports for each age group is as follows: Under age 20 Age 20-29 Age 30 or older 68 92 140 a. Do the data indicate that the distribution of accidents for the three age groups is significantly different from the distribution of drivers? Test with =.05. b. Write a sentence demonstrating how the outcome of the hypothesis test would appear in a research report. 9. A researcher would like to know whether there is a consistent, predictable relationship between verbal skills and math skills for high school students. A sample of 200 students is obtained, and each student is given a standardized English test and a standardized math test. Based on the test results, students are classified as high or low for verbal skills and math skills. The results are summarized in the following frequency distribution: Verbal Skills High Low 59 41 31 69 High Math 100 Low Math 100 90 110 n = 200 a. Based on the results, can the researcher conclude that there is a significant relationship between verbal skills and math skills? Test at the =.05 level of significance. b. Compute the phi-coefficient to measure the strength of the relationship. 10. Gender differences in dream content are well documented (see Winget & Kramer, 1979). Suppose a researcher studies aggression content in the dreams of men and women. Each participant reports his or her most recent dream. Then each dream is judged by a panel of experts to have low, medium, or high aggression content. The observed frequencies are shown in the following matrix: Aggression Content Low Medium High 18 4 2 4 17 15 Female Gender Male a. Is there a relationship between gender and the aggression content of dreams? Test with =.01. Extra Credit (+1) For the following data: a. Find the regression equation for predicting Y from X. b. Use the regression equation to find a predicted Y for each X. c. Find the difference between the actual Y value and the predicted Y value for each individual, square the differences, and add the squared values to obtain SSresidual. d. Calculate the Pearson correlation for these data. Use r2 and SSY to compute SSresidual. You should obtain the same value as in part c. X Y 5 10 3 6 6 7 4 3 2 4