STAT 200 Week 6 Homework

 #1 9.1.2

Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology exam 84,199 of them were female. In that same year, of the 211,693 students who took the calculus AB exam 102,598 of them were female ("AP exam scores," 2013). 

Estimate the difference in the proportion of female students taking the biology exam and female students taking the calculus AB exam using a 90% confidence level.

a.) State the random variables and the parameters in words.

b.) State and check the assumptions for confidence interval.

c.) Find the sample statistics and confidence interval of the difference

d.) Provide a statistical interpretation of the confidence interval

e.) Provide a real-world Interpretation of the confidence interval

#2 9.1.5

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.

a.) State the random variables and the parameters in words.

b.) State the null and alternative hypotheses and the level of significance

c.) State and check the assumptions for a hypothesis test

d.) Find the sample statistics, test statistic, and p-value

e.) State the statistical conclusion (in terms of accepting or rejecting the null hypothesis)

f.) Provide a real-world interpretation of the results of the hypothesis test

  

#3 9.3.3

A study was conducted that measured the total brain volume (TBV) (in mm3) of patients that had schizophrenia and patients that are considered normal. Table #9.3.5 contains the TBV of the normal patients and table #9.3.6 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.

a.) State the random variables and the parameters in words.

b.) State the null and alternative hypotheses and the level of significance

c.) State and check the assumptions for the hypothesis test

d.) Find the sample statistic, test statistic, and p-value

e.) State the statistical conclusion (in terms of accepting or rejecting the null hypothesis)

f.) Provide a real-world interpretation of the results of the hypothesis test

Table #9.3.5: 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 #9.3.6: 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

#4 11.3.4

A study was undertaken to see how accurate food labeling for calories on food that is considered reduced calorie. The group measured the amount of calories for each item of food and then found the percent difference between measured and labeled food. 

The group also looked at food that was nationally advertised, regionally distributed, or locally prepared. 

The data are in table #11.3.5 ("Calories datafile," 2013). 

Do the data indicate that at least two of the mean percent differences between the three groups are different? 

Test at the 10% level.

a.) State the random variables and the parameters in words

b.) State the null and alternative hypotheses and the level of significance

c.) State and check the assumptions for the hypothesis test

d.) Find the test statistic and p-value

e.) State the statistical conclusion (in terms of accepting or rejecting the null hypothesis)

f.) Provide a real-world interpretation of the results of the hypothesis test

Table #11.3.5: Percent Differences Between Measured and Labeled Food

  

National Advertised Regionally Distributed Locally Prepared

 

   2           41        15

-28           46        60           

  -6             2      250

   8           25      145

   6           39          6

  -1        16.5        80

 10           17        95

 13           28          3

 15            -3

  -4           14

  -4           34

-18           42

 10

   5

   3

  -7

   3  

-0.5

-10

   6