Question 7
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 #1 contains the TBV of the normal patients and Table #2 contains the TBV of schizophrenia patients ("SOCR data Oct2009," 2013).
Table #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 #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 |
Let ?1= mean TBV of patients that are considered normal. Let ?2 = mean TBV of patients that had schizophrenia. Compute a 90% confidence interval for the difference in TBV of normal patients and patients with Schizophrenia.
(i) For the sample from population with mean = ?1 : Determine sample mean x??1 and sample standard deviation s1
Enter sample mean to nearest integer, then comma, then sample standard deviation to nearest integer. Examples of correctly entered answers:
1332,112
-15478,3651
(ii) For the sample from the population with mean = ?2 : Determine sample mean x??2 and samplestandard deviation s2
Enter sample mean to nearest integer, then comma, then sample standard deviation to nearest integer. Examples of correctly entered answers:
1332,112
-15478,3651
(iii) Enter the level of significance ? used for this test:
Enter in decimal form. Examples of correctly entered answers: 0.01 0.02 0.05 0.10
(iv) Determine degrees of freedom df :
Enter value rounded DOWN to nearest integer.
(v) Determine t - score associated with critical value: tc
Enter in decimal form to nearest thousandth. Examples of correctly entered answers:
0.0011 0.020 0.500 0.371 2.000
(vi) Determine "error bound of the mean" E
Enter value rounded to nearest integer.
(vii) Determine confidence interval estimate of the difference ?1 – ?2:
Enter lower bound value to nearest integer, followed by < , followed by "?1-?2" for difference, followed by <, followed by upper bound value to nearest integer. No spaces between any characters. Do not use italics, but if mathematically necessary use negative signs. Examples of correctly entered answers:
0.77<?1-?2<0.78
13.12<?1-?2<13.94
-9.73<?1-?2<-8.08
(viii) Using the confidence interval, select the most correct description of the result of the survey:
A. We estimate with 90% confidence that the mean TBV of people considered normal is anywhere from 51565 mm3 more to 75657 mm3 less than the mean TBV for people with schizophrenia.
B. We estimate with 90% confidence that the true proportional TBV of people considered normal is anywhere from 51565 mm3 less to 75657 mm3 more than the mean TBV for people with schizophrenia.
C. We estimate with 90% confidence that the sample mean TBV of people considered normal is anywhere from 51565 mm3 less to 75657 mm3 more than the mean TBV for people with schizophrenia.
D. We estimate with 90% confidence that the true mean TBV of people considered normal is anywhere from 51565 mm3 less to 75657 mm3 more than the mean TBV for people with schizophrenia.
Enter letter corresponding to most correct answer
We have to find 90% confidence interval of .
(i) The sample mean and standard deviation is given by
(ii)
(iii)
The level of significance is 0.10
(iv)
The degree of freedom is
(v) t-score= 1.670
(vi) Error bound of the mean is given by
(vii)
(viii)
D. We estimate with 90% confidence that the true mean TBV of people considered normal is anywhere from 51565 mm3 less to 75657 mm3 more than the mean TBV for people with schizophrenia.
Get Answers For Free
Most questions answered within 1 hours.