Question/PSP

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.

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.