Question

You plan to take a random sample of 1000 undergraduate students enrolled at the

University of Rochester to compare the proportion of female and male students who

would like to see that the United States of America have a female President.

b.Suppose that you use random numbers to select students, but you stop

selecting females as soon as you have 100, and you stop selecting males once you

have 100. Is the resulting sample a simple random sample? Why or why not ?

c.What type of sample is the sample in part b?What advantages might

it have over simple random sampling?

Answer 1

b)

Now the resulting sampling is not as simple random sampling

Simple random sampling is a sample of individuals that exist in a population; the individuals are randomly selected from the population and placed into a sample. But here are diviiding our population in two gropus or strata i.e Females and Males , and we stop selecting females as soon as you have 100 ,and stop selecting males as soon as you have 100 , so these may not be the case of simple random sampling as population is our our population is divided into two smaller groups known as strata ( via Males and Females ).

If this was Simple random sampling then we would have selected randomly any students regardless of there gender.

c.What type of sample is the sample in part b?What advantages might

it have over simple random sampling?

This is Stratified random sampling in part b.

Stratified random sampling is a method of sampling that involves the division of a population into smaller sub-groups known as strata .

Stratified random sampling is also called proportional random sampling or quota random sampling.

In stratified random sampling or stratification, the strata are formed based on members' shared attributes or characteristics such as income or educational attainment or Gender etc.

Here we use characteristics of Gender ( Males Or Female ) , hence Stratified random sampling.

Stratified random sampling differs from simple random sampling, which involves the random selection of data from an entire population, so each possible sample is equally likely to occur.

A stratified random sample can provide greater precision than a simple random sample of the same size. Because it provides greater precision, a stratified sample often requires a smaller sample, which saves money

As if we are selecting students by using simple random sampling , then our result might get biased due to the fact that if we have more number of female students , then they may favour to have an Female President . So selecting samples based on their attributes or characteristics like Gendr is important here .

So Stratified random sampling is better in than simple random sampling, in these case