Question

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?

Answer 1

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

Explanation:

Always use the 4 Steps for Inference Testing:

STEP 1:
State your hypothesis.

`H_o: p_1-p_2=0`
`H_a: p_1-p_2ne0`

STEP 2:
State your test statistic, conditions and significance

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

`hatp_1=277/1524` , `hatp_2=246/1545`, `hatp=(277+246)/(1524+1545)`

Check Condition:
`n_1hatp_1=277` and `n_1(1-hatp_1)=1247`
`n_2hatp_2=246` and `n_2(1-hatp_2)=1299`

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

STEP 3
Perform the inference test.

`z=(277/1524-246/1545)/sqrt((277+246)/(1524+1545))=1.66rArr` P-value `=0.0969`

STEP 4
State your conclusions

Because P > 0.01, do not reject the null hypothesis. There is insufficient evidence that there is difference in treatment outcome with ginko.

99% Confidence Interval (z=2.576)

`hatp_1-hatp_2+-zsqrt((hatp_1(1-hatp_1))/n_1+(hatp_2(1-hatp_2))/n_2` `=(-0.0124, 0.0575)`

This is consistent with the z-test as you will note that the value of zero is included in the confidence range indicating that there is no evidence that the population proportions are different from zero.

Hope that helped