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, 50 subjects wore magnetic insoles and 38 subjects wore nonmagnetic insoles. The results are shown at the right. At -07 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. Complete parts (a) through (e) Do you Yes 19 No 31 .es 20 No 18 The claim is "the proportion of subjects who feel better with magnetic inscles is Let pl represent the population proportion for the magnetic insoles and p2·epresent the population pr por Choose the correct answer below I those who feel better we' nonmagnetic nsoles." s for ho mo agefK Indes Suta OB, Ho : p1

Explanation / Answer

The hypothesis is

H0: P1 = P2
Ha: P1 P2

Hence C

we are given that
p1 = 19/50 = 0.38
n1 = 50

p2 = 20/38 = 0.53
n2 = 38

Since the null hypothesis states that P1=P2, we use a pooled sample proportion (p) to compute the standard error of the sampling distribution.
p = (p1 * n1 + p2 * n2) / (n1 + n2)

= (0.38*50 +0.53*38)/(88) = 0.44

Compute the standard error (SE) of the sampling distribution difference between two proportions.
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

sqrt( 0.44 * ( 1 - 0.44 ) * ( (1/50) + (1/38) ) )
= 0.1068

The test statistic is a z-score (z) defined by the following equation.
z = (p1 - p2) / SE

Z = (0.38-0.53)/0.1068 = -1.404

The critical value of z at alpha = 0.07 is
-1.4758 from the z table

as the z stat is not greater than z critcal hence we fail to reject the null hypothesis as test stat is not in the rejection region

hence at 7% signficance level , there is insufficient evidence to support the claim

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