Question

Determine whether the following statement regarding the hypothesistest for two population proportions is true or false.
However small the difference between two population proportion ,for sufficiently large sample size, the null hypothesis of equalpopulation proportions is likely to be rejected.

Answer 1

Answer:

False

Step-by-step explanation:

Let p1 be the population proportion for the first population

and p2 be the population proportion for the second population

Then

$H_{0}$ p1  = p2

$H_{a}$ p1 ≠ p2

Test statistic can be found usin the equation:

$z=\frac{p1-p2}{\sqrt{{p*(1-p)*(\frac{1}{n1} +\frac{1}{n2}) }}}$ where

• p1 is the sample population proportion for the first population

• p2 is the sample population proportion for the second population

• p is the pool proportion of p1 and p2

• n1 is the sample size of the first population

• n2 is the sample size of the second population.

As |p1-p2| gets smaller, the value of the test statistic gets smaller. Thus the probability of its being extreme gets smaller. This means its p-value gets higher.

As the p-value gets higher, the null hypothesis is less likely be rejected.