Question

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.

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

Answer 1

In order to solve this question I used Excel.

Step.1 Enter data in excel sheet.

Step.2 Go to 'Data' menu ---> 'Data Analysis' ---> Select 't Test :Assuming unequal variances'.

Step.3 New window will pop-up on screen. Refer following screen shot and enter information accordingly.

Excel output:

Schizophrenia	Normal
1331777	1663407		Variance of schi	29560690487
1368378	1453510		Variance of normal	15739779000
1690182	1474790
1563593	1441636		t-Test: Two-Sample Assuming Unequal Variances
1325525	1574808
1636119	1512571			Schizophrenia	Normal
1487886	1583940		Mean	1451293.194	1463339.219
1476891	1650348		Variance	29560690487	15739779000
1569413	1317156		Observations	31	32
1317885	1432033		Hypothesized Mean Difference	0
1588573	1502702		df	55
1066075	1635918		t Stat	-0.316842857
1443775	1299470		P(T<=t) one-tail	0.376281198
1177002	1288971		t Critical one-tail	1.673033966
1420249	1441045		P(T<=t) two-tail	0.752562396
1476254	1420416		t Critical two-tail	2.004044769
1297327	1203344
1337827	1535137
1387893	1366346
1363859	1463498
1648209	1480171
1499983	1319737
1658258	1431890
1483763	1326402
1238979	1650207
1354054	1360810
1861991	1688990
1588132	1578698
1688950	1503005
1286638	1523045
1354649	1410213
	1292641

Hypothesis:

Since p-value for one tailed test is 0.3763 which is greater than 0.10,hence we accept null hypothesis and conclude that the patients with schizophrenia have approximately equal TBV on average than a patient that is considered normal.