Respuesta :
The test statistic value for the given sample data with population mean difference is equal to optic C. 3.156.
As given in the question,
Given population mean difference μd = 0
sample size 'n' = 9
Sample data is:
x y [tex]d_{i}[/tex] ( x - y) [tex]( d_{i} - \bar{d} )^{2}[/tex]
168 162 6 15.21
180 178 2 62.41
157 145 12 4.41
132 125 7 8.41
202 171 31 445.21
124 126 -2 141.61
190 180 10 0.01
210 195 15 26.01
171 163 8 3.61
∑[tex]d_{i}[/tex] = 89 ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] = 706.89
[tex]\bar{d}[/tex] = ( 1/ n ) ∑[tex]d_{i}[/tex]
= (1/9) (89)
= 9.889
= 9.9
Standard deviation of the mean difference '[tex]S_{d}[/tex]'
= √[1 / (n - 1)]( ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] )
= √706.89/ 8
=√88.361
= 9.4
test statistic
t = ( [tex]\bar{d}[/tex] - μd)/ ( [tex]s_{d} /\sqrt{n}[/tex] )
= ( 9.9 - 0) / ( 9.4 / √9)
= 9.9/ 3.133
= 3.156
Therefore, the test statistic value for the given sample data is equal to option C. 3.156
Learn more about test statistic here
brainly.com/question/14128303
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