Question

What is the observed value of the test​ statistic? (Find the test statistic for ModifyingAbove p with caret 1minusModifyingAbove p with caret 2​, where ModifyingAbove p with caret 1 is the proportion over the sample of people using the nicotine gum and ModifyingAbove p with caret 2 is the proportion over the sample of people using the​ placebo.)

Answer 1

Answer:

The test statistic is $z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{P(1-P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}$.

Step-by-step explanation:

The test statistic for hypothesis test for the significant difference between two proportions is:

$z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{P(1-P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}$

The combined proportions P is computed using the formula:

$P=\frac{n_{1}\hat p_{1}+n_{2}\hat p_{2}}{n_{1}+n_{2}}$

Here,

Sample 1 represents the proportion over the sample of people using the nicotine gum.

Sample 2 represents the proportion over the sample of people using the​ placebo.