A simple random sample (SRS) of 150 is taken from a population with a 0.6 proportion of success. An independent SRS of 250 is taken from a population with a 0.3 proportion of success. What is the standard deviation of the sampling distribution for the difference in sample proportions?

Step-by-step explanation:

For this case we have the following data:

represent the random sample 1 selected

represent the proportion of success for the sample 1 selected

represent the random sample 2 selected

represent the proportion of success for the sample 2 selected

We know for this case that we can use the normal approximation since for both cases we have:

We have the randomization condition and we assume that the two samples are <10% of the entire population size.

So then we can use the following distribution for the proportions:

For this case we want to find the distribution for the difference of these two proportions and we have this:

So then the dtandard deviation would be given by:

idk

step-by-step explanation: