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iGreen
 one year ago
Hypothesis Testing
iGreen
 one year ago
Hypothesis Testing

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iGreen
 one year ago
Best ResponseYou've already chosen the best response.0I just need help finding the Test Statistic and Pvalue

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The study mentions proportions of patients responding to the treatment, so that's what your test should be concerned with. The t.s. for a proportion can be derived from the usual \(Z\) t.s.: \[Z=\frac{\bar{x}\mu_0}{\sigma}=\frac{n\hat{p}np_0}{\sqrt{np_0(1p_0)}}=\frac{\hat{p}p_0}{\sqrt{\dfrac{p_0(1p_0)}{n}}}\] where \(p_0\) is the proportion assumed under the null hypothesis.

iGreen
 one year ago
Best ResponseYou've already chosen the best response.0Hmm..so how would I set this up?

iGreen
 one year ago
Best ResponseYou've already chosen the best response.0Like, what do \(\sf \hat{p}, p_0,\) and \(\sf n\) stand for?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Prior to the treatment, you have a mortality rate of \(60\%\), so this is \(p_0\). The study shows a mortality rate of \(\hat{p}=\dfrac{36}{87}\approx0.4138\). Right away you also know the sample size is \(n=87\).

iGreen
 one year ago
Best ResponseYou've already chosen the best response.0So I have: \(\sf \dfrac{0.4138  0.6}{\sqrt{\dfrac{0.6(1  0.6)}{87}}} \approx 3.55 \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right, now to find the \(p\) value you can refer to a \(z\) table, or if you're looking for better accuracy you might want to use a calculator to compute the area under the distribution curve.

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.0Also note: \[H_0 = null\ hypothesis\] \[H_1 = Research\ Hypothesis\]

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.0The hypothesis is since the new treatment reduces deaths The null hypothesis is the new treatment doesn't reduce deaths

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This computation shows that the critical value is \(Z_{\alpha/2}=Z_{0.005}\approx2.5758\): http://www.wolframalpha.com/input/?i=Solve%5BIntegrate%5BPDF%5BNormalDistribution%5B0%2C1%5D%2Cx%5D%2C%7Bx%2Ct%2Ct%7D%5D%3D%3D.99%2Ct%5D In order to reject the null hypothesis, you need the test statistic \(Z\) to satisfy \(Z>2.5758\), which is clearly the case. This computation approximates the exact \(p\) value: http://www.wolframalpha.com/input/?i=Integrate%5BPDF%5BNormalDistribution%5B0%2C1%5D%2Cx%5D%2C%7Bx%2CInfinity%2C3.5453%7D%5D (I've included this because the typical \(z\) table doesn't provide the same level of precision.)
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