MAT209 Exam 1 Name__________________________1. 10 points An instructor was curious about which route would get her to school faster. Between Oct. 2 and Nov. 15, she collected data on how long the trip took for a freeway route and for a through-town route. When she approached the turning point, if her odometer (which reports how many miles the car has traveled in its life) ended in an even number she took the freeway route and if an odd number she took the through-town route. A. Describe the response variable and indicate if it is quantitative or categorical.B. Describe the explanatory variable and indicate if it is quantitative or categorical.C. Would you consider this an observational study or an experiment? Explain why (clearly differentiating the two types of studies)D. Suppose the instructor finds a significant difference between these two routes. Would she have been able to conclude that the faster time to campus was due to the route? Explain.2. 6 points The correlation between two random variables was found to be exactly 1. Check any of the following that would be true, regarding the corresponding scatterplot?___ The slope of the best fitting line would be 1. ___ Every point would lie along a perfect straight line, with no deviations at all. ___ The best fitting line would have an uphill (positive slope). 3. 4 points Suppose you wanted to conduct a study to compare two medical treatments on people with a specific medical condition. Previous research suggests that a person’s current medical condition might berelated to their age, sex, previous medical history, body mass index (a measure combining weight and height), and smoking behavior. You are told by your statistical consultant to randomly assign the subjectsin your study to two groups, so that one treatment may be randomly assigned to each group. A friend asks why you wouldn't be better off forcing the groups to be balanced with respect to the characteristics listed above, instead of leaving it to chance to make the groups comparable. How would you answer yourfriend?4. 5 points Suppose that weights of bags of potato chips coming from a factory follow a normal distribution with mean 12.8 ounces and standard deviation .6 ounces. If the manufacturer wants to keepthe mean at 12.8 ounces but adjust the standard deviation so that only 1% of the bags weigh less than 12 ounces, how small does he/she need to make that standard deviation? 6. 17 points In a study of whethera relationship exists between achild's aptitude and the age atwhich he/she first speaks,researchers recorded the age (inmonths) of a child's first speechand the child's score on anaptitude test. The data for these21 children is shown in thetable. The value of thecorrelation coefficient is -0.640.The scatterplot displays thisrelationship. Variable Mean StDev x 14.38 7.95 y 93.67 13.99 A. Calculate the least squares line for predicting aptitude score from age at first speech.B. What proportion of the variability in aptitude scores is explained by the least squares line with age at firstspeech?C. Calculate the residual for child 16.D. Judging from the scatterplot, which child has the largest (in absolute value) residual? Is this child also the most influential observation? Why or why not?E. Would you recommend using this relationship to predict the food expenditure for a household with an income of $5,200. Why or why not?7. 5 points P(A) = .4 and P( A or B) = .8 For what value of P(B) are A and B independent?8. 5 points When the oil is low, a car’s oil light goes on 98% of the time. However, even when the oillevel is o.k., the light will go on 1% of the time. Assume that the probability that the oil is really low is 10%. What is the probability that a driver needs to be concerned if the oil light goes on?9. 5 points A local grocery store is having a random drawing. Each week Sheri has a 35% chance of winning a free gallon of milk. If Sheri plays for 6 consecutive weeks, what is the probability that she never wins a free gallon of milk? We can assume that each week is independent from the