TreatmentShamResearchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table forthe treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. Assume thatthe two samples are independent simple random samples selected from normally distributed populations, and do not assume that thepopulation standard deviations are equal. Complete parts (a) and (b) below.Ini28280.510.440.771.09a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.What are the null and alternative hypotheses?O A. Ho: H1 H2O C. Ho: H1 * H2H1: H1

Given;(a) In order to test whether treatment with magnets is effective or not we will consider the following hypothesis: H0:μ1=μ2H1:μ1>μ2 Therefore correct option is b Since we have been given that the population standard deviations are equal we will use pooled variance to calculate the test statistics. Pooled variance =Sp2=(n1-1)S12+(n2-1) S22n1+n2-1=(28-1)0.772+(28-1)1.09228+28-2=0.8905Threfore test statistics =X1-X2Sp21n1+1n2~tn1+n2-2=0.51-0.440.8905128+128=0.28 P value =0.39 At 0.05 significance level (α)and with 54 degrees of freedom the acceptance region of null is below 1.6735 and since our test statistics lie in this region we will accept the null hypothesis . Therefore there is not sufficient evidence to prove the claim treatment with magnets is effective in reducing back pain. Yes it is valid to say that magnets might appear to be more effective as increasing sizes will lead to increase in test statistics value which can lead to rejection of null and acceptance of alternate according to which the treatment is effective Since sample mean of treatment with magnets is more than that of sham treatment we can say that the it is possible to argue that if the sample size increases the treatment with magnets might become effective (b) The 95 % confidence interval is =X1-X2 ± tα2,n1+n2-2 Sp21n1+1n2=0.51-0.44 ±2.005 0.8905128+128=( -0.436 ; 0.576 )Therefore -0.436 <μ1-μ2 <0.576

Math

Statistics

a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. What are the null and alternative hypotheses? O A. Ho: H1 H2 OD. Ho: H1 = P2 OC. Ho: H1 + H2 H1: H1

a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. What are the null and alternative hypotheses? O A. Ho: H1 H2 OD. Ho: H1 = P2 OC. Ho: H1 + H2 H1: H1

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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