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# Biostatistics Problem to Reject or Accept Hypothesis

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I have attached a long regression problem that I completed most of. I'd like you to tell me what I did wrong including incorrect calculations. Comments and hints would be also be greatly appreciated as I am just learning this. I know this is a long problem so Im offering 12 credits. Thanks.

I have attached the problem as it was given to me (without my work) first. Then I attached my completed copy.
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Assignment A, Module 3
Please fill in all of the blank spaces below. Due May 17, 2004. (15 points)
Obs# X Y X2 Y2 XY YCALC = a + bX YOBS - YCALC
1 22 120
2 20 115
3 23 100
4 21 100
5 20 110
6 24 145
7 24 140
8 27 180
9 23 125
10 28 210
11 23 120
12 26 160
13 25 150
14 29 225
15 30 200
16 28 175
17 27 180
18 23 130

:
Mean
n = number of X-Y pairs = (X)2 = (Y)2 =
df = (number of paired observations) - 2 = n - 2 =
b = {(XY) - [(X)(Y)/n]} =
(X2) - (X)2/n
or
b = {[n((XY))] - [(X)(Y)]}/{[n((X2))] - [(X)2]}
=

or
b = SSXY/SSX = ([(XY)] - [(X)(Y)/n])/([ (X2)] - [(X)2/n]) =

SSXY = [(XY)] - [(X)(Y)/n] =
SSX = [(X2)] - [(X)2/n] =

a = YMEAN - b(XMEAN) =

YCALC =

Module 3 Assignment A (Page 2)

Obs#
X
Y xi =
Xi - meanX
xi2 yi =
Yi - meanY
yi2
xiyi
1 22 120
2 20 115
3 23 100
4 21 100
5 20 110
6 24 145
7 24 140
8 27 180
9 23 125
10 28 210
11 23 120
12 26 160
13 25 150
14 29 225
15 30 200
16 28 175
17 27 180
18 23 130

:
Mean
s2
s

(sx)2 = [(Xi - meanX)2]/(n - 1) = [(xi2)]/(n - 1) =
(sy)2 = [(Yi - meanY)2]/(n - 1) = [(yi2)]/(n - 1) =
(sy·x)2 = (n - 1)[(sy)2 - (b2)(sx)2]/(n - 2) =

(sa)2 = [(sy·x)2/n] + {[(sy·x)2(meanX)2]/[(n - 1)(sx)2]}
=

sa =

(sb)2 = (sy·x)2/[(n - 1)(sx)2] =

sb =

Module 3 Assignment A (page 3):

Ho: b = 0.0000 : 0.05

tCALC = b/sb = df = n - 2 =

tTABLE(0.05) = therefore reject or fail to reject Ho that b = 0.0000 (choose one)

95% CI for b: b ± (tTABLE)(sb) =

therefore, 95% CI for b:
therefore, reject or fail to reject Ho that b = 0.000 (choose one)

...............
Ho: b = 1.0000 : 0.05

tCALC = (b - 1.0000)/sb =

tTABLE = therefore reject or fail to reject Ho that b = 1.0000 (choose one)

95% CI for b: b ± (tTABLE)(sb) =

therefore, 95% CI for b:
therefore, reject or fail to reject Ho that b = 1.0000 (choose one)

..............
Ho: b = 0.0000 : 0.05

FCALC = MS(R)/MS(E) = SS(R)/MS(E) = (b2)(SSX)/MS(E)
=

MS(E) = SS(E)/(n - 2) =
(or, MS(E) = [(sb)2](SSX) =
SS(E) = SS(TOTAL) - SS(R) =
SS(R) = (b2)(SSX) =
SS(TOTAL) = SSY = [(Y2)] - [(Y)2/n] =

FTable; 0.05; 1, (n - 2) = therefore reject or fail to reject Ho that b = 0.0000 (choose one)

Module 3 Assignment A (page 4):

95% Confidence Interval for regression line (at a given value of X):

95% CI: yCALC ± [(ttable)(syCALC)]

(syCALC)2 = [(sy·x)2/n] + {[(sy·x)2(X - meanX)2]/[(n - 1)(sx)2]}

if X = 28.6111:

(syCALC)2 =

(syCALC) =

YCALC =

yCALC ± [(ttable)(syCALC)] =

95% CI:

Module 3 Assignment A (page 5):

95% Confidence Interval for an individual calculated value of Y:

If, once the regression line has been calculated from a set of X-Y observations, it is desired to calculate Y for an individual whose value of X is 28.6111, the 95% CI for that individual's calculated value of Y is: yCALC ± [(ttable)(syNEW)]

(syNEW)2 = (sy·x)2 + [(sy·x)2/n] + {[(sy·x)2(X - meanX)2]/[(n - 1)(sx)2]}
=

(syNEW) =

YCALC =

yCALC ± [(ttable)(syNEW)] =

95% CI:

Module 3 Assignment A (page 6):

r = {(XY) - [(X)(Y)/n]} =
{[(X2) - (X)2/n] [(Y2) - (Y)2/n]}1/2

or
r = [(X - meanX)(Y - meanY)]/{[ (X - meanX)2][ (Y - meanY)2]}1/2
= [(xiyi)]/{[(xi2)][(yi2)]}1/2 =

or
r = (b)(sx)/(sy) =
or
r = SSXY/{(SSX)(SSY)}1/2 =

Ho: r = 0.0000 : 0.05

tCALC = r/sr =

sr = {(1 - r2)/(n - 2)}1/2 =

tTABLE(0.05) = therefore reject or fail to reject Ho that r = 0.000 (choose one)

...............
using table values for r:

Ho: r = 0.0000 : 0.05 rTABLE(0.05) =

therefore reject or fail to reject Ho that r = 0.0000 (choose one)

................
Using F-ratio for regression:

FCALC = MS(R)/MS(E) = SS(R)/MS(E) = (b2)(SSX)/MS(E)
=
FTable(0.05) =
therefore reject or fail to Ho that r = 0.0000 (choose one)

##### Solution Summary

The expert examines biostatistic problems to reject or accept hypothesis tests. The F-ratio for regression is used.

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