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Math 221 **** Example Format **** Week 2 Lab Submitted by: (Insert Name Here **REMOVE THIS NOTE PRIOR TO SUBMITTING**) (Note: Your labs should be well organized, with results clearly identified and in the proper order. When answering questions, be sure to use complete sentences and proper grammar. It is also important for you to fully explain your answers! Please do not answer “yes” (or “no”); you should explain why the answer is “yes”. **REMOVE THIS NOTE PRIOR TO SUBMITTING**) Part 1. Random Sampling Ordered Sample AA AF AK AO AP AQ AR AV AX AY BJ BO BQ BV CD CE CG CI CN CV The auditor should randomly select files because there is a cost-benefit tradeoff. It takes too much time and money to audit all the files. Knowing how to take a random sample and make inferences about the population is an essential tool for auditing. Part 2. Cereal and Fiber Type Cereals By Fiber/Serving Low Fiber Medium Fiber Frequency High Fiber 0 10 20 30 40 Cereals By Fiber/Serving High Fiber Medium Fiber Low Fiber Part 3. Milk Production 1. Find the sample mean. 2270.54 2. Find the sample standard deviation. 653.18 3. Make a frequency distribution for the data. Distribution is started at right. Milk Production Class Limits 1147 1646 1647 2146 2147 2646 2647 3146 Frequency 7 15 13 11 Midpoint 1396.5 1896.5 2396.5 2896.5 Cumulative Frequency 7 22 35 46 3147 3647 4147 3646 4146 4646 3 0 1 3396.5 3896.5 4396.5 49 49 50 4. Create a histogram for the data. Does the data appear bell-shaped? Milk Production 16 14 12 10 8 6 4 2 0 1646 2146 2646 3146 3646 4146 4646 No. The data appears to be skewed to the right. 5. What true percent of the data lies within one standard deviations of the mean? Within two standard deviations of the mean? How do these results agree with the Empirical Rule? Within one standard deviation, 74% (Empirical rule says 68%) Within two standard deviations, 98% (Empirical rule says 95%) These results aren’t exactly the same as the empirical rule, but they are very close. 6. Find the median of the milk production. 2207 7. Find the maximum and the minimum value. Minimum: 1147, Maximum: 4285 8. What is the range? 3138 9. What is the first Quartile? 1798.25 10. What is the second Quartile? (What is this also called?) This is also called the median. 2207 11. What is the third Quartile? 2727.5 12. What is the 80th percentile? 2812.4 Part 4. Linear Regression Sugar and Calories Analysis Sugar and Calories 300 Calories 250 y = 4.0934x + 105.03 200 r = 0.552 150 100 50 0 0 10 20 30 Sugar There is a moderate positive relationship between sugar and calories. Sugar and Cost Analysis Sugar and Cost 60 50 y = 0.6987x + 20.791 Cost 40 r = 0.471 30 20 10 0 0 10 20 30 Sugar There is a moderate positive relationship between sugar and cost. Weight and Cost Analysis Weight and Cost 60 y = 16.971x + 3.3162 50 Cost 40 r = 0.831 30 20 10 0 0.00 1.00 2.00 3.00 Weight There is a strong positive relationship between weight and cost. (Place your answers in the appropriate position. Format them so that they are clearly shown. See the worksheet Linear Regressionfrom the Week2Lab.xls file for details. Be sure to follow the examples given in the files linked from our course for detailed instructions. Be sure to answer all questions using complete sentences and clearly explain yourself. **REMOVE THIS NOTE PRIOR TO SUBMITTING**)