1. A week-long study of weight change, exercise and caloric intake was conducted among a sample of members at a local gym. The variables are as follows:
   DV = weight change in pounds during the week
   IV ₁ = mean number of hours of aerobic exercise each day
   IV ₂ = mean number of calories eaten each day
   Note that weight change is defined as the difference between one’s weight at the beginning of the week and one’s weight at the end of the week. A positive value indicates one lost weight at the end of the week (e.g., weight at start = 300, weight at end = 250, difference = 300 – 250 = 50 lbs lost). In the study, all participants lost weight, so scores on the DV are all positive. Note that a negative value indicates one would gain weight during the week.
   Results of the regression analysis follow.
   Table 8: Regression of Weight Loss on Hours of Exercise and Caloric Intake
   Variable b se b 95% CI
   Hours of Exercise 0.27 0.11 0.05, 0.49
   Caloric Intake -0.002 .0008 -0.0035, -0.0004
   Intercept 8.50 0.73 7.05, 9.95
   Note: R ² = .35, adj. R ² = .35, F = 22.18, df = 2,117; n = 120
   (a). Which predictors of weight loss are statistically significant, if either?
   (b). What is the predicted weight loss for someone who consumes 2,000 calories per day, on average, and exercises 1 hour per day on average?
   (c). What is the predicted weight loss for someone who consumes 3,000 calories per day, on average, and exercises 30 minutes (0.5 hour) per day?
   (d). What is the literal interpretation for the slope of hours of aerobic exercise (b ₁ = -0.27)?
   (e). What is the literal interpretation for the slope of total calories eaten (b ₂ = -0.002)?
   (f). What is the literal interpretation for the intercept (b ₀ = 8.50)?
   (g). What is the interpretation of R ² = .35 for weight loss in pounds during the week of study?
   (h). Assume the F ratio of 22.18 is statistically significant. What does rejection of the null hypothesis associated with this test tell us?
2. Over the past few years, 225 students enrolled in sections of GOV 1111 have completed the final test of three tests administered in that course. The overall mean is 81.9 with a standard deviation of 11.2. These data are nearly normal in distribution; given this, answer the following:
   (a). What percentage of students will score 87.5 or higher on this test?
   (b). What percentage of students will score lower than 73.5?
   (c). What percentage of students will score higher than 98.7?
   (d). What is the percentile rank for a student with a score of 81.9?
   (e). What is the percentile rank for a student with a score of 59.5?
   (f). What is the percentile rank for a student with a score of 76.3?
   (g). What is the raw test 3 score for a student with a z score of -1.5?
   (h). What is the raw test 3 score for a student with a z score of 0.75?
   (i). What is the raw test 3 score for a student with a z score of 0.00?
3. For each of the following, indicate whether the decision regarding the null hypothesis is reject or fail to reject, the type of error possible, and the probability of this error. When needed, assume a = .05.
   Obtained Test Information Decision, reject Type of error? Probability of
   Statistic or fail to reject? this error?
   1. F = 0.03 Critical F = 4.95 _____ ____
      (b) r = -.23 Critical r = ≠ .41 ____ ________
      (c) r = -.01 p-value = .04 ____ ______________
      (d) x ² = 6.81 Critical x ² = 9.81 ______ _____________
      (e) t = -2.56 Critical t = ≠ 2.59 _____ __________
      (f) 95% CI of mean, H _O : μ = 4.8 ______ ___
      4.0 to 7.1
4. Assume a researcher wishes to compare student mathematics performance on a standardized test among three 6 ^th grade teachers: Ms. White, Ms. Jones, and Ms. Hill. The researcher will use ANOVA to first determine if there are differences in mean mathematics scores among the three teachers, and if there are significant differences, then the researcher will perform multiple comparisons to examine the following pairwise comparisons:

Pairwise comparisons of Mean Mathematics Scores

1. Ms. White vs. Ms. Jones
2. Ms. White vs. Ms. Hill
3. Ms. Jones vs. Ms. Hill

1. Suppose the ANOVA results indicated significant mean differences in mathematics scores among the three teachers. Next, the researcher must conduct pairwise comparisons. The researcher sets the overall Type 1 error rate to α = .10 due to the small sample sizes of students within each class. Using the Type 1 error rate of α = .10 for each pairwise comparison, what would be the inflated familywise error rate for the three pairwise comparisons for this unadjusted α of .10? That is, what would be probability of committing at least one Type 1 error across the family of tests for these pairwise comparisons if the per comparison α is .10?
2. Lastly, suppose the researcher finds the familywise error rate calculated in "a" above to be too large for comfort and decides to use the Bonferroni correction for the pairwise comparisons. If the overall family wise α = .10, what would be the per comparison Bonferroni corrected α for each pairwise comparison?

For the following (5, 6 and 7 ), create an APA styled results presentation. This will include a table of results, and written inference and interpretation.

1. Is there a difference in mean humidity levels among the three states of Utah, Minnesota, and Georgia? Humidity was recorded in the early morning (12:58am) of 14 June 2013 in five randomly selected towns in each of the three states. Humidity readings were taken from www.wunderground.com . Data are presented below:
   Georgia: 76%, 85%, 93%, 96%, 77%
   Minnesota: 67%, 68%, 65%, 73%, 73%
   Utah: 21%, 26%, 13%, 43%, 36%
2. Does mean level of humidity appear to differ during the day in Georgia? Below are humidity levels recorded for certain cities in Georgia. The data were recorded at 7:00am and again at 4:00pm. Does the afternoon humidity level differ from the morning humidity level?
   Place Morning Afternoon
   Athens 85% 52%
   Atlanta 82% 52%
   Augusta 87% 49%
   Columbus 87% 51%
   Macon 87% 50%
   Savannah 86% 54%
3. This item taken from a textbook:

"Criminologists have long debated whether there is [an association] between weather and violent crime. The author of the article "Is There a Season for Homicide?" ( Criminology (1988): 287-296) classified [1352] homicides according to season, resulting in the accompany data."

Results of the author’s study found the following counts of homicide in the population studied: winter = 311, spring = 320, summer = 401, and fall = 320.

Does it appear that homicide counts differ by season?

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