In a study of the effectiveness of a fabric device that acts like a support stoc

Question

In a study of the effectiveness of a fabric device that acts like a support stocking for a weak or damaged heart, 110 people who consented to treatment were assigned at random to either a standard treatment consisting of drugs or the experimental treatment that consisted of drugs plus surgery to install the stocking. After two years, 45% of the 60 patients receiving the stocking had improved and 38% of the patients receiving the standard treatment had improved. (Use a statistical computer package to calculate the P-value. Use pexperimental pstandard. Round your test statistic to two decimal places and your P-value to four decimal places.)

Do these data provide convincing evidence that the proportion of patients who improve is higher for the experimental treatment than for the standard treatment? Test the relevant hypotheses using a significance level of 0.05.

Yes

No   

Explanation / Answer

Solution:

H0: p1-p2=0 (the proportions of success under both procedures are the same
Ha: p1 –p2 0 (the proportions are not the same)

z = [(p1 – p2) – 0]/ sqrt [p1q1/n1 + p2q2/n2]
= [(0.45– 0.38) – 0]/ sqrt [(0.45)(0.55)/60+ (0.38)(0.62)/50]
=( 0.45-0.38)/ 0.094 = 0.74

Using Excel to get the p-value (level of significance), = 1 - normsdist(0.74) = 0.2297

P = 0.2297 (Round the answer to four decimal places.)
Yes
0.2297 > 0.05
At this significance level, I would not reject the null hypothesis, that the two treatments are the same.

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