# 1545 subjects were given ginko & 1524 placebo. In ginko group, 246 developed dementian & in the placebo it was 277 with dementia. Significance level=0.01 to test claim(ginko is effective in dementia) Can you test claim and construct confidence interval?

Oct 11, 2015

Deb - This is an inference test for the difference between 2-population proportions

#### Explanation:

Always use the 4 Steps for Inference Testing:

STEP 1:

${H}_{o} : {p}_{1} - {p}_{2} = 0$
${H}_{a} : {p}_{1} - {p}_{2} \ne 0$

STEP 2:
State your test statistic, conditions and significance

We will use a 2-proportion z-test at $\alpha = 0.01$

${\hat{p}}_{1} = \frac{277}{1524}$ , ${\hat{p}}_{2} = \frac{246}{1545}$, $\hat{p} = \frac{277 + 246}{1524 + 1545}$

Check Condition:
${n}_{1} {\hat{p}}_{1} = 277$ and ${n}_{1} \left(1 - {\hat{p}}_{1}\right) = 1247$
${n}_{2} {\hat{p}}_{2} = 246$ and ${n}_{2} \left(1 - {\hat{p}}_{2}\right) = 1299$

All values are greater than 5 , so the condition is met.

STEP 3
Perform the inference test.

$z = \frac{\frac{277}{1524} - \frac{246}{1545}}{\sqrt{\frac{277 + 246}{1524 + 1545}}} = 1.66 \Rightarrow$ P-value $= 0.0969$

STEP 4
hatp_1-hatp_2+-zsqrt((hatp_1(1-hatp_1))/n_1+(hatp_2(1-hatp_2))/n_2 $= \left(- 0.0124 , 0.0575\right)$