Question

A study was conducted that measured the total brain volume (TBV) (in ) 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.

Table #9.3.5: Total Brain Volume (in ) 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 ) 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

Answer 1

A study was conducted that measured the total brain volume (TBV) (in ) 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.

Let Group1 = Normal

     Group2 = Schizophrenia

Ho: µ₁ = µ₂   H₁: µ₁ > µ₂

Upper tail test used.

Calculated test statistic t = 0.3184

DF = n₁+n₂-2 =61

Table value of t with 61 DF at 0.10 level = 1.2956

Rejection Region: Reject Ho if t > 1.2956

Calculated t = 0.3184, not in the rejection region

The null hypothesis is not rejected.

There is not enough evidence to conclude that the patients with schizophrenia have less TBV on average than a patient that is considered normal.

calculations:

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.1
Normal 1 Sample
Sample Size	32
Sample Mean	1463339.219
Sample Standard Deviation	125458.2759
Schizophrenia 2 Sample
Sample Size	31
Sample Mean	1451293.194
Sample Standard Deviation	171932.2264
Intermediate Calculations
1 Sample Degrees of Freedom	31
2 Sample Degrees of Freedom	30
Total Degrees of Freedom	61
Pooled Variance	22536948583.7099
Standard Error	37832.2347
Difference in Sample Means	12046.0252
t Test Statistic	0.3184
Upper-Tail Test
Upper Critical Value	1.2956
p-Value	0.3756
Do not reject the null hypothesis