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[Solved] Suppose 40 children, both of whose parents smoke, and 50 children, neither of whose parents smoke, are recruited for the study. How much power

Question: Suppose 40 children, both of whose parents smoke, and 50 children, neither of whose parents smoke, are recruited for the study.

How much power would such a study have using a two-sided test with significance level \(\alpha=.05\), assuming that the estimates of the population parameters in the pilot study are correct?

In this case, we calculate

\[Power=\Pr \left( \frac{{{{\bar{X}}}_{1}}-{{{\bar{X}}}_{2}}}{\sqrt{\frac{{{0.4}^{2}}}{50}+\frac{{{0.7}^{2}}}{40}}}<-1.96\text{ or }\,\frac{{{{\bar{X}}}_{1}}-{{{\bar{X}}}_{2}}}{\sqrt{\frac{{{0.4}^{2}}}{50}+\frac{{{0.7}^{2}}}{40}}}>1.96 \right)\] \[=\Pr \left( Z-\frac{0.2}{\sqrt{\frac{{{0.4}^{2}}}{50}+\frac{{{0.7}^{2}}}{40}}}<-1.96\text{ or }\,Z-\frac{0.2}{\sqrt{\frac{{{0.4}^{2}}}{50}+\frac{{{0.7}^{2}}}{40}}}>1.96 \right)\] \[=\Pr \left( Z-\frac{0.2}{0.124298}<-1.96\text{ or }\,Z-\frac{0.2}{0.124298}>1.96 \right)\] \[=\Pr \left( Z<-0.35096 \right)+\Pr \left( Z>3.569036 \right)=0.363\]

8.73:

Ten patients with advanced diabetic nephropathy (kidney complications of diabetes) were treated with captopril over an 8-week period [10]. Urinary protein was measured be

fore and after drug therapy1 with results listed in Table 8.2 in both the raw and ln scale.

Perform the test in Problem $8.72$ using both the raw and ln scale, and report a $p$ -value. Are there any advantages in using the raw or the ln scale?

Price: $2.99
Solution: The downloadable solution consists of 4 pages
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