Stat 500 Midterm Exam Questions And Correct Answers 2023.
Stat 500 MIDTERM EXAM QUESTIONS AND CORRECT ANSWERS 2023. Name:_ SOLUTIONS (8 questions) YOU HAVE 3 HOURS TO COMPLETE THIS. Show all work. Just showing answer without calculations may result in a zero for that question. 1. A water-heater manufacturer guarantees the electric heating element for a period of five years. The lifetimes, in months, for a sample of 10 such elements are as follows. 49.3 79.3 186.4 68.4 62.6 65.1 53.2 32.3 40.1 29.3 A. (10 points) Using the methods we learned in class, identify the five number summary for this set of data. Ordered data: 29.3 32.3 40.1 49.3 53.2 62.6 65.1 68.4 79.3 186.4 Min = 29.3; Max = 186.4 Median position = (n+1) /2 = 5.5; So, Median = Average of 5th and 6th observation = (53.2+62.6)/2 = 57.9 Q1 position = (n+1) /4 = 2.75; So, Q1 = 2nd observation + (0.75)*(3rd observation – 2nd observation) = 32.3 + (0.75)*(40.1 – 32.3) = 38.15 Q3 position =3* (n+1) /4 = 8.25; So, Q1 = 8th observation + (0.72)*(9th observation – 8th observation) = 68.4 + (0.25)*(79.3 – 68.4) = 71.125 Five Number Summary: (29.3, 38.15, 57.9, 71.13, 186.4) B. (5 points) Using the boxplot method we learned in class, are there any potential outliers? If so, what value(s) are they? IQR = Q3 – Q1 = 71.125 – 38.15 = -11.313 (1.5)*IQR = 49.463 Q1 – 49.463 = 21.662
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