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The function f is continuous on the closed interval [1,15] and has the values shown on the table above. Let g(x) = ∫f(t) dt [1,x]. Using the intervals [1,3], [3,6], [6,10], [10,15], what is the approximation of g(15) – g(1) obtained from a left Riemann Sum? t: 1 3 6 10 15 f(t) 2 3 4 2 -1

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Do the levels of fear in children change over time? If so, in what ways? Very little research has been done on the prevalence and persistence of fears in children. Researchers surveyed a group of third and fourth grade children and asked them to rate their level of fear about a variety of situations. After two years the children again completed the same survey. The researchers calculated the mean fear rating for each child in both years and were interested in the relation between these ratings. The least-squares regression line for the data, with 89 mean fear ratings as the explanatory variable and 91 mean fear ratings as the response variable, is given below. Dependent variable is 91 means R squared = 27.4% S = 0.2374 with 94 ? 2 = 92 degrees of freedom Variable Coefficient s.e. of coefficient t-ratio P-value Constant 0.877917 0.1184 7.42 ¡Ü 0.0001 89 means 0.397911 0.0676 5.89 ¡Ü 0.0001 Approximately what is a 95% confidence interval for the slope of the least squares regression line? Choose one answer. A. (0.26, 0.54) B. (0.76, 1) C. (0.74, 1.02) D. (0.33, 0.47) E. (0.38, 0.42) How about this one? Do the levels of fear in children change over time? If so, in what ways? Very little research has been done on the prevalence and persistence of fears in children. Researchers surveyed a group of third and fourth grade children and asked them to rate their level of fear about a variety of situations. After two years the children again completed the same survey. The researchers calculated the mean fear rating for each child in both years and were interested in the relation between these ratings. The least-squares regression line for the data, with 89 mean fear ratings as the explanatory variable and 91 mean fear ratings as the response variable, is given below. Dependent variable is 91 means R squared = 27.4% S = 0.2374 with 94 ? 2 = 92 degrees of freedom Variable Coefficient s.e. of coefficient t-ratio P-value Constant 0.877917 0.1184 7.42 ¡Ü 0.0001 89 means 0.397911 0.0676 5.89 ¡Ü 0.0001 Using the above data, approximately what is the intercept of the least squares regression line? Choose one answer. A. 0.40 B. 0.44 C. 0.88 D. 0.12 E. 0.07 Great! How about this one? At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are bundled in clothes to restrict their movement? Data was collected from parents who brought their babies to New York University Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported ages (in weeks) at which their child was first able to crawl a distance of four feet within one minute. The researchers also recorded the average outdoor temperature (in F) 6 months after the babies’ date of birth. The resulting data were grouped by month of birth and all data for babies born on a given month averaged together. If we fit the least-squares line to the 12 data points (one for each month), we obtain the following results from a software package. Notice that the temperature given is taken as the explanatory variable and crawling age as the response variable. Dependent variable is the average crawling age R squared = 49.0% S = 1.319 with 12 ? 2 = 10 degrees of freedom Variable Coefficient S.E. of coefficient Constant 35.6781 1.318 Temperature-0.077739 0.0251 What is the approximate slope of the least-squares regression line? Choose one answer. A. 35.68 B. 1.32 C. 0.01 D. -0.08 E. -0.58 Could mud wrestling be the cause of a rash contracted by Washington State University students in the spring of 1992? Physicians at the WSU student health center wondered this when one male and six female students complained of rashes after participating in a mud wrestling event. Questionnaires were sent to all students in the residence halls that participated in the event. The questionnaire asked about the appearance of a rash and about attendance at the event. The results are summarized below: Men Women Developed Rash 12 12 No Rash 38 12 What is the p-value for the chi-square statistic? Choose one answer. A. Between 0.05 and 0.01 B. Larger than 0.10 C. Between 0.10 and 0.05 D. Less than 0.01 E. Between 0.001 and 0.01

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