M1 solns and REMARKS

# 1 the x variable is exam score and its units are

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1. The X variable is Exam Score, and its units are POINTS. The Y variable is Study Time and its units are HOURS. It is incorrect to list variables as units. Exam Score per Hours Studying is incorrect. 2. Also, we always interpret slope as change in Y per ONE UNIT CHANGE IN X. For example, the slope in the coffee/temperature was -554. This means for EVERY ONE DEGREE increase in temperature, coffee sales went down by 554. For the exam scores problem, the correct answer is points earned per EACH (ONE) hour studying . Points per HourS studying is not correct. Note that “Hours Studying” is a variable, not a unit. It reflects the number of hours the person studied. In the case of cars, the proper unit is miles per gallon. It is not miles per gallons. The slope is miles traveled PER EACH GALLON used. 3. Partial credit was given as deemed appropriate. 33. The TREATMENTS of an experiment are the combinations of values of the factor that are randomly assigned to the subjects. 34. Suppose a manufacturer has recorded its cost of electricity (in dollars) and the total number of hours of machine time for their factory during a certain number of weeks. They want to use the data to estimate electric bills based on machine time. Their data analysis is below. The average cost for electricity per week is known to be \$1041.90. What is the average amount of machine time? Include units. Show your work. X = machine time; Y = cost Given: Y-bar = 1041.9; want to find X bar Regression equation is Y = 263.4 + 71.654 X The point (X bar, Y bar) is on every regression line Plug in 1041.9 for Y bar in the regression equation and solve for X bar to get 1041.9 = 263.4 + 71.654(x bar) = 10.86 HOURS Descriptive Statistics: Time, Cost Variable N StDev Variance Minimum Q1 Median Time 52 2.664 7.099 6.000 8.000 11.000 Cost 52 258.9 67043.1 464.3 879.2 1018.8 6

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Variable Q3 Maximum Time 13.000 15.000 Cost 1243.2 1598.1 Regression Analysis Predictor Coef SE Coef T P Constant 263.4 103.8 2.54 0.014 Time 71.654 9.284 7.72 0.000 35. Bob is doing a survey of Columbus residents to find out their opinions on having a casino built downtown. He takes a random sample of names from the Columbus phone book. His sampling plan contains bias due to UNDERCOVERAGE . 1. “Convenience sample” or “Voluntary sample” are incorrect here, because a RANDOM sample was taken. There was a plan for the sample, it was not just done out of convenience. The problem is that a group of individuals, namely those who are not in the phone book for whatever reason, had no chance of being chosen. 2. It is important to be able to use the proper and precise statistical terminology when identifying and describing problems you find regarding samples and analyses. This is a term we used quite often in the class, in Recitation, and on HW. Variations of this term (subject to spelling errors) could not be accepted. Use this info for problems 36-37: Suppose managers know that the average number of contacts they make with their clients is 10 per year. They also know the average number of sales per client per year is 652 units. Now they want to predict the number of sales using the number of contacts. Their analysis is below (n = 50).
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