I do not understand how to solve these two questions, please show the correct an

Question

I do not understand how to solve these two questions, please show the correct answers and calculation work where necessary. The biggest problem that I have is finding the p-value so it would be really helpful if you can explain how to solve it along with the sample statistic. Really appreciate the help! Thanks.

Chapter 4, Section 2, Exercise 068 If You Break an Arm, Use Your Brain! Multiple studies are helping us understand the power of the mind on the body. One such study1 examines the effect of imagery on muscle strength. In the study, 29 healthy individuals underwent four weeks of wrist immobilization to induce weakness. Half of the participants were randomly assigned to mentally imagine strong muscle contractions in that arm (without actually moving the arm.) At the end of the four weeks, the percentage decrease in muscle strength was measured for all the participants, and we are testing to see if mean decrease is greater for people who do not use mental imaging when muscles are immobilized than for people who do. For the 15 participants not using any mental imagery, the mean percent decrease in muscle strength was 51.2 while for the 14 ticipants using imagery, it was 24.5. A randomization distribution of differences in means (mean decrease with no imagery minus mean decrease with imagery) using 1000 simulated samples is shown in the figure below. Let group 1 be those who do no imagery and let group 2 be those who do imagery 30 20 10 0 -30 -25 -20 15 10 10 15 20 25 null = 0 Clark BC, et al., "The power of the mind: the cortex as a critical determinant of muscle strength/weakness," J Neurophysiol, 112: 32193226, October, 2014

Explanation / Answer

Q2. Proportion Data
PART 1.
Ho: p1 < p2 , H1: p1 > p2

PART 2:
given that,
sample one, x1 =4, n1 =10, p1= x1/n1=0.4
sample two, x2 =1, n2 =14, p2= x2/n2=0.071
p1 - p2 = (0.4-0.071)= -0.31
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.4-0.071)/sqrt((0.208*0.792(1/10+1/14))
zo =1.954
| zo | =1.954
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =1.954 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 1.9541 ) = 0.02535
hence value of p0.05 > 0.02535,here we reject Ho
test statistic: 1.954
critical value: 1.645
decision: reject Ho
p-value: 0.02535

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