Answer to Question #178011 in Statistics and Probability for Calvin Lee

Question #178011

A new drug cures 9 of 200 patients suffering from a type of cancer, for which the historical cure rate is 2%. Perform a test to check on the significance of this result, at both 5% and 1% levels of significance. Based on your conclusion, comments on the efficacy of the treatment using this new drug. 


1
Expert's answer
2021-04-15T07:39:43-0400

"H_0 : p = 0.02 \\\\\n\nH_1 : p \u2260 0.02 \\\\\n\nn = 200 \\\\\n\n\\bar{p} = \\frac{9}{200} = 0.045 \\\\\n\n\u03b1_1 = 0.05"

Test statistic:

"Z = \\frac{ \\bar{p} -p}{\\sqrt{ \\frac{p(1-p)}{n}}} \\\\\n\nZ = \\frac{ 0.045 -0.02}{\\sqrt{ \\frac{(0.02)(0.08)}{200}}} = 2.53"

Critical value:

"\u03a6(Z_{cr}) = \\frac{1 -\u03b1_1}{2} = 0.475 \\\\\n\nZ_{cr}=1.96"

(−∞,−1.96) "\\cup" (1.96,∞) is the rejection region.

The test statistic Z falls into the rejection region. So we reject H0 and accept H1.

The efficacy of the treatment using this new drug is not equal to 2%.

"\u03b1_2 = 0.01 \\\\\n\n\u03a6(Z_{cr}) = \\frac{1 -\u03b1_2}{2} = 0.495 \\\\\n\nZ_{cr}=2.58"

(−∞,−2.58) "\\cup" (2.58,∞) is the rejection region.

The test statistic Z does not fall into the rejection region. So we accept H0.

The efficacy of the treatment using this new drug is equal to 2%.


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