Statistics Homework Exam Preparation

Exam 2 MPA 625—Statistics Name:__________________ March, 2023 Instructor: Dr. Mark Wilson Note: you can use your book and notes. Do not contact anybody in class during the test period. Instructions: Answer all questions and show calculations where necessary. Type answers into this Word doc and email your completed exam to me by 8pm. Please shrink graphs. Good luck. Part 1. Short Answer (type answers into this document). 1. Why is the standard normal table found in the back jacket of nearly every statistics book in print? How does the standard normal distribution compare with a “normal distribution”? (5 pts.) 2. Explain this: X⁓N(20, 6). (5 points) 3. What is the usefulness of the Empirical Rule? (5 pts.) 4. The weight of West Virginia males is normally distributed with a mean of 196 pounds. Twenty-five percent of males weigh less than 174 pounds. Find the standard deviation. (5 points) hint: Z = (X*-Xbar / s). 5. How can we use the notion of “degrees of freedom” in everyday life? (5 points) Part 2. Computation 6. An airline examined jumbo-jet passengers to see if age was associated with seat choice. Fill-in the crosstabs below. (25 pts.) a. Complete the crosstabs table. Label fully. First Class Business Class Coach Class Seniors (65+) 12 56 144 Adults (18-65) 15 61 181 Kids (1-17) 3 15 45 b. Find P(senior); find P(kid) c. Find P(Bus Class and kid); find P(Coach class and Adult) d. Find P(Senior|Coach); Find P(Coach|Senior) e. Are airline seats nominal, ordinal, interval or ratio level data? Explain in one sentence. f. Put this table in Minitab and test the hypothesis that age is related to seat choice. Make sure to state the null and alternative hypotheses. 7. Open the attached Excel spreadsheet and paste the data into Minitab. (25 points) Light bulb burn times may follow a normal distribution. Find data in the column “Burn Hours.” a. Find the mean and standard deviation of this sample. b. Put the burn hours histogram here _____. Explain whether or not it’s a normal distribution. How did you make your determination? c. Find the cutoff (in hrs.) for the lower quarter of light bulb burn times. d. Find the range for the middle 50% of burn times. e. Find the cutoff for the lowest 15% of burn times. 8. Interpreting the standard normal distribution. (12 points) Calculate the area left of 1.1. Calculate the area from -0.6 to 1.8. Use the Empirical Rule to estimate the area to the left of 1 added to the area to the right of 2. 1 1 Exam 2 MPA 625 — Statistics Name:__________________ M arch , 202 3 Instructor: Dr. Mark Wilson N ote : you can use your book and notes. D o not contact anybody in class during the test period. Instructions: Answer all questions and s how calculation s where necessary. Type answers into this Word doc and e mail your completed exam to me by 8pm . Please shrink graphs. Good luck. Part 1. Short Answer (type answers into this document). 1. W hy is the standard normal table found in the back jacket of nearly every statistics book in print ? How does the standard normal distribution compare with a “normal distribution”? ( 5 pts.) 2. Explain this: X ? N( 2 0, 6 ). (5 points) 3. W hat is the usefulness of the E mpirical R ule ? ( 5 pts.) 4. The weight of West Virginia males is normal ly distributed with a mean of 19 6 pounds. T wenty - five percent of males weigh less than 1 74 pounds. Find the s tandard deviation . (5 points) h int : Z = ( X * - X bar / s ) . 5. H ow can we use the notion of “ degrees of freedom ” in every day life ? ( 5 points) 1 Exam 2 MPA 625—Statistics Name:__________________ March, 2023 Instructor: Dr. Mark Wilson Note: you can use your book and notes. Do not contact anybody in class during the test period. Instructions: Answer all questions and show calculations where necessary. Type answers into this Word doc and email your completed exam to me by 8pm. Please shrink graphs. Good luck. Part 1. Short Answer (type answers into this document). 1. Why is the standard normal table found in the back jacket of nearly every statistics book in print? How does the standard normal distribution compare with a “normal distribution”? (5 pts.) 2. Explain this: X?N(20, 6). (5 points) 3. What is the usefulness of the Empirical Rule? (5 pts.) 4. The weight of West Virginia males is normally distributed with a mean of 196 pounds. Twenty-five percent of males weigh less than 174 pounds. Find the standard deviation. (5 points) hint: Z = (X*-Xbar / s). 5. How can we use the notion of “degrees of freedom” in everyday life? (5 points) Sheet1 Hours Measures the time 60W bulbs burn until failure 1215.79 1071.83 1231.25 1224.03 1145.04 1237.43 1141.86 1352.61 1044.33 1234.77 1114.9 1356.04 1256.22 1295.33 1243.79 1255.62 1263.61 1327.04 1370.65 1177.6 1130.55 1335.57 1160.07 1257.08 1329.73 1286.74 1155.73 1070.7 1271.07 1155.32 1273.69 1317.31 1150.15 1208.5 1314.87 1282.07 1276.57 1229.51 1300.3 1177.32 1160.95 1093.36 1135.16 1359.03 1184.25 1123.07 1319.46 1208.55 1149.76 1355.47 1240.46 1282.83 1223.81 1248.94 1267.17 1256 1341.08 1510.35 1256.53 1262.41 1187.32 1342.02 1346.65 1422.32 1166.29 1356.84 1235.8 1413.94 1244.2 1286.64 1130.44 1281.16 1247.88 1291.82 1225.07 1214.48 1227.56 1295.73 1296.05 1287.07 1210.13 1262.04 1238.68 1240.36 1358.89 1201.33 1319.96 1330.31 1200.4 1274.12 1255.55 1243.11 1267.78 1151.56 1203.85 1239.09 1263.95 1459.85 1108.45 1250.5 1215.79 1071.83 1231.25 1224.03 1145.04 1239.43 1181.86 1352.61 1044.33 1234.77 1111.49 1336.04 1256.22 1295.33 1243.79 1255.62 1270.61 1327.04 1340.65 1177.6 1130.55 1350.57 1170.07 1257.08 1329.73 1286.74 1155.73 1075.7 1271.07 1155.32 1273.69 1317.31 1150.15 1204.5 1314.87 1282.07 1276.57 1229.51 1310.3 1177.32 1160.95 1093.36 1135.16 1379.03 1184.25 1123.07 1319.46 1208.55 1169.76 1335.47 1240.46 1242.83 1223.81 1248.94 1267.17 1296 1341.08 1510.35 1256.53 1265.41 1187.32 1342.02 1336.65 1422.32 1176.29 1356.84 1235.8 1413.94 1240.2 1286.64 1130.44 1281.16 1247.88 1299.82 1225.07 1214.48 1227.56 1295.73 1296.05 1280.07 1210.13 1262.04 1238.68 1240.36 1358.89 1201.33 1319.96 1330.31 1220.4 1274.12 1255.55 1243.11 1267.78 1151.56 1203.85 1239.09 1263.95 1459.85 1108.45 1257.5