Winter17-Math1342-ONLINE-CRN 12490 Hector Hernandez 1H/18 8:14 P- Quiz: Quiz: RE

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Winter17-Math1342-ONLINE-CRN 12490 Hector Hernandez 1H/18 8:14 P- Quiz: Quiz: REVIEW for EXAM4 -Chp 8-thru-10 Submit Q This Question: 1 pt 45 of 53 This Quiz: 53 pts poss Question Help Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo populations, and do not assume that the population standard deviations are )group. The resuts are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed equal. Complete parts (a) and (b) below Use a 0.05 significance level for both parts 0.54 068 0.43 a. 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 ahernative hypotheses? The test statistic, tis0.28) (Round to two decimal places as needed) The P-value is0.781 (Round to three decimal places as needed) State the conclusion for the test. Fail to reject the nul hypothesis. There is not sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment Isrtvalid to argue that magnets mugt appear to be eflectivo the sample sizes are larger? Since the sample sizes are larger for those reated with magnets is the samp e mean for those g en a shamtreatmen" vadtoangu" that may es- appear to be efe bette Click to select your answerls) Save for Later

Explanation / Answer

Treatment

Sham

µ

µ1

µ2

n

13

13

x

0.54

0.43

s

0.68

1.23

To test whether the magnet treatment has a greater mean reduction in pain than sham treatment.

B)

H0 : µ1= µ2

H1: µ1> µ2

t = (x1 – x2)/[(s21 /n1) + (s22 /n2)]

=(0.54-0.43)/ [(0.682 /13) + (1.232 /13)]

=0.28219

Degrees of freedom=n-1=12 (since sample sizes are equal)

P-value for one tailed test using R software:

> pt(0.28,12)

[1] 0.6078772

Fail to reject the null hypothesis. There is no sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given sham treatment.

Since the sample mean for those treated with magnets is equal to the sample mean for those given a sham treatment, it is valid to argue that magnets might appear to be effective is the sample size is larger.

Confidence interval:

95% confidence interval is given by: (x1 – x2) ± t * standard error

Where t is the table value at desired level

MSE = (s21 + s22­) / 2 = 0.98765

Standard error= [(2*MSE)/n] (since sample sizes are same)

= 0.3898

t0.05,12 = 1.782

95% confidence interval is given by: (x1 – x2) ± t * standard error

95% confidence interval is given by: 0.11 ± 1.782 * 0.3898

95% confidence interval is given by: (-0.5846, 0.80462)

95% confidence interval is given by: -0.5846 < µ1- µ2 <0.80462

Treatment

Sham

µ

µ1

µ2

n

13

13

x

0.54

0.43

s

0.68

1.23

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