7CA 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 Patients16634071583940129947015351371431890157869814535101650348128897113663461326402150300514747901317156144104514634981650207152304514416361432033142041614801711360810141021315748081502702120334413197371688990129264115125711635918 Table #2: Total Brain Volume (in mm3) of Schizophrenia Patients1331777148788610660751297327149998318619911368378147689114437751337827165825815881321690182156941311770021387893148376316889501563593131788514202491363859123897912866381325525158857314762541648209135405413546491636119 Let μ1 = mean TBV of patients that are considered normal. Let μ2 = mean TBV of patients that had schizophrenia. Compute a 90% confidence interval for the difference in TBV of normal patients and patients with Schizophrenia. (vii) Determine confidence interval estimate of the difference μ1 – μ2 :Enter lower bound value to nearest integer, followed by < , followed by "μ1-μ2" 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<μ1-μ2<0.7813.12<μ1-μ2<13.94-9.73<μ1-μ2<-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

Solution To find the interval we will use the t distribution.

Answered: A study was conducted that measured the…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2AGP

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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 μ₁ = mean TBV of patients that are considered normal. Let μ₂ = mean TBV of patients that had schizophrenia. Compute a 90% confidence interval for the difference in TBV of normal patients and patients with Schizophrenia.

(vii) Determine confidence interval estimate of the difference μ₁ – μ₂ :

Enter lower bound value to nearest integer, followed by < , followed by "μ1-μ2" 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<μ1-μ2<0.78

13.12<μ1-μ2<13.94

-9.73<μ1-μ2<-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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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