STAT 200 Week 6 Homework Problems Please type your answers to these questions in this document using FULL SENTENCES, showing your work and/or including your reasoning. Save your work as a Word or .rtf...

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STAT 200 Week 6 Homework Problems Please type your answers to these questions in this document using FULL SENTENCES, showing your work and/or including your reasoning. Save your work as a Word or .rtf file (NO “.pages”, please!) with file name “YourLastName_HW6”. Attach your file to the Assignment link and submit your work before 11:59 pm on Tuesday of Week 6. Question/PSP Score 1. Are there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that are mostly rural? In the state of Pennsylvania, a fairly urban state, there are 245 eight-year-olds diagnosed with ASD out of 18,440 eight-year-olds evaluated. In the state of Utah, a fairly rural state, there are 45 eight-year-olds diagnosed with ASD out of 2,123 eight-year-olds evaluated ("Autism and developmental," 2008). Is there enough evidence to show that the proportion of children diagnosed with ASD in Pennsylvania is more than the proportion in Utah? Test at the 1% level. Step 1: State the question Step 2: Identify the information a. State the random variables and parameters in words b. State the null and alternative hypotheses and level of significance c. Determine the type of test this is, then state and check the assumptions for this type of test Step 3: Perform calculations a. Find the sample statistics b. Find the test statistic c. Find the p-value d. State the conclusion (compare p and alpha and decide to reject Ho or fail to reject Ho) Step 4. Interpret (answer the original question in a complete sentence) 2. A study was conducted that measured the total brain volume (TBV) (in mm3) of patients that had schizophrenia and patients that are considered normal. Table #3.1 contains the TBV of the normal patients and table #3.1 contains the TBV of schizophrenia patients ("SOCR data oct2009," 2013). Is there enough evidence to show that the patients with schizophrenia have less TBV on average than a patient that is considered normal? Test at the 10% level. Table #3.1: Total Brain Volume (in mm3) of Normal Patients 1663407 1583940 1299470 1535137 1431890 1578698 1453510 1650348 1288971 1366346 1326402 1503005 1474790 1317156 1441045 1463498 1650207 1523045 1441636 1432033 1420416 1480171 1360810 1410213 1574808 1502702 1203344 1319737 1688990 1292641 1512571 1635918 Table #3.2: Total Brain Volume (in mm3) of Schizophrenia Patients 1331777 1487886 1066075 1297327 1499983 1861991 1368378 1476891 1443775 1337827 1658258 1588132 1690182 1569413 1177002 1387893 1483763 1688950 1563593 1317885 1420249 1363859 1238979 1286638 1325525 1588573 1476254 1648209 1354054 1354649 1636119 Step 1: State the question Step 2: Identify the information a. State the random variables and parameters in words b. State the null and alternative hypotheses and level of significance c. Determine the type of test this is, then state and check the assumptions for this type of test Step 3: Perform calculations a. Find the sample statistics b. Find the test statistic c. Find the p-value d. State the conclusion (compare p and alpha and decide to reject Ho or fail to reject Ho) Step 4. Interpret (answer the original question in a complete sentence) 3. A study was conducted that measured the total brain volume (TBV) (in mm3) of patients that had schizophrenia and patients that are considered normal. The tables in question 3 contain the TBV of the normal patients and the TBV of schizophrenia patients ("SOCR data oct2009," 2013). Compute a 90% confidence interval for the difference in TBV of normal patients and patients with Schizophrenia. Show your work, including the critical value, margin of error, results statement, and interpretation of results. 4. Levi-Strauss Co manufactures clothing. The quality control department measures weekly values of different suppliers (i.e. plants) for the percentage difference of waste between the layout on the computer and the actual waste when the clothing is made (called run-up). The data is in the table below, and there are some negative values because sometimes the supplier is able to layout the pattern better than the computer ("Waste run up," 2013). Do the data show that there is a difference between some of the suppliers? Test at the 1% level. Table #5: Run-ups for Different Plants Making Levi Strauss Clothing Plant 1 Plant 2 Plant 3 Plant 4 Plant 5 1.2 16.4 12.1 11.5 24 10.1 -6 9.7 10.2 -3.7 -2 -11.6 7.4 3.8 8.2 1.5 -1.3 -2.1 8.3 9.2 -3 4 10.1 6.6 -9.3 -0.7 17 4.7 10.2 8 3.2 3.8 4.6 8.8 15.8 2.7 4.3 3.9 2.7 22.3 -3.2 10.4 3.6 5.1 3.1 -1.7 4.2 9.6 11.2 16.8 2.4 8.5 9.8 5.9 11.3 0.3 6.3 6.5 13 12.3 3.5 9 5.7 6.8 16.9 -0.8 7.1 5.1 14.5 19.4 4.3 3.4 5.2 2.8 19.7 -0.8 7.3 13 3 -3.9 7.1 42.7 7.6 0.9 3.4 1.4 70.2 1.5 0.7 3 8.5 2.4 6 1.3 2.9