# 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.