In a 4-week study about the effectiveness of using magnetic insoles to treat pla

Question

In a 4-week study about the effectiveness of using magnetic insoles to treat plantar heel pain, 56 subjects wore magnetic insoles and 47 subjects wore nonmagnetic insoles. The results are shown at the right. At alpha equals =0.09, can you support the claim that there is a difference in the proportion of subjects who feel better between the two groups? Assume the random samples are independent Do you Feel Better? Magnetic Insoles Yes 18 No 38 Nonmagnetic Insoles Yes 19 No 28

Find the standardized test statistic.

Explanation / Answer

Null, There Is No Significance between them Ho: p1 = p2
Alternate, difference in the proportion of subjects
who feel better between the two groups H1: p1 != p2
Test Statistic
Sample 1 : X1 =18, n1 =56, P1= X1/n1=0.321
Sample 2 : X2 =19, n2 =47, P2= X2/n2=0.404
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.359
Q^ Value For Proportion= 1-P^=0.641
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.321-0.404)/Sqrt((0.359*0.641(1/56+1/47))
Zo =-0.873
| Zo | =0.873
Critical Value
The Value of |Z | at LOS 0.09% is 1.695
We got |Zo| =0.873 & | Z | =1.695
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -0.8727 ) = 0.3828
Hence Value of P0.09 < 0.3828,Here We Do not Reject Ho

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