A medical researcher gives a new muscle relaxant to 200 patients and determines

Question

A medical researcher gives a new muscle relaxant to 200 patients and determines that 156 have beneficial results. The muscle relaxants currently in use have a success rate of 0.7. Test whether the new drug is superior to the existing drugs. a) Choose the null hypothesis, by recording the letter of your choice from below H0: p = 0.78 H0: p = 0.7 H0: p > 0.78 H0: p > 0.7 b) Choose the alternative hypothesis, by recording the letter of your choice from below Ha: p = 0.78 Ha: p > 0.7 Ha: p > 0.78 Ha: p > 0.7 c) What is the value of the test statistic? Give your answer to two digits past the decimal. d) What is the P value or significance probability? Give your answer to 3 places past the decimal, without a leading zero. e) Choose the appropriate conclusion. no evidence against the null hypothesis weak evidence against the null hypothesis strong evidence against the null hypothesis very strong evidence against the null hypothesis

Explanation / Answer

a) H0: p = 0.7. Hypothesis testing is done considering null hypothesis to be true and since the drug currently in use has a success rate of 0.7, we consider the null hypothesis to be 0.7

b) Ha: p > 0.7, Hypothesis testing is done to find if there is sufficient evidence to support a particular claim. Here the claim is that the new drug is superior than the old drug. Hence the greater than symbol.

c) Standard deviation, = sqrt[ P * ( 1 - P ) / n ], where P is the hypothesized value of population proportion in the null hypothesis, and n is the sample size.
= sqrt[0.7*(1-0.7)/200] = 0.0324037

Test statistic, z = (p - P) / = ((156/200) - 0.7)/0.0324037 = 2.47

d) p value = .007

e) Strong evidence against the null hypothesis, since the probability is only 0.7%.

Very strong evidence would be used if the p-value is less than 0.001.

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