Question

writing a end of week summary....what is inference for one proportion vs inference for two proportion?

Answer 1

One proportion:

If we wanted to test whether the sample proportion is equal to population proportion or an assumed number then we use one proportion. For example: the prevalence of a disease X is to known to be 20%. To check if the same is true in the collected sample we use one proportion. Once the samples are collected we calculate the proportion from that sample and using the z-test for single proportion we test if there is any significant difference between sample and population proportion. The null hypothesis that we test here will be defined as H0: There is no significant difference between sample and population proportion, Sample proportion = 0.20 against the alternative hypothesis H1: Sample proportion is significantly different from 0.20. After doing the z-test we either reject or accept the null hypothesis and infer if the sample proportion is statistically significantly different from 0.20.

Two proportion:

In the two proportion, we compare samples proportions from two groups. For example, if the researcher is interested to know whether the prevalence of disease X is same between females and males he collects the sample of proportions from males and females and tests the difference using z-test for two proportions. Here the null hypothesis is defined as H0: The prevalence of the disease is equal among females and males against the alternative hypothesis H1: There prevalence of the disease are not equal among females and males. After the testing, we infer if there is a significant difference in the prevalence among female and males.