Question

In two common species of flowers, A and B, the proportions of flowers that are blue are  and  , respectively. Suppose that independent random samples of 50 species-A flowers and 100 species-B flowers are selected. Let  be the sample proportion of blue species-A flowers and  be the sample proportion of blue species-B flowers. What is the mean of the sampling distribution of 

Answer 1

Pa - Pb

Explanation:

The mean of the distribution of sample differences will always be the difference between the population proportion, That is ; Pa - Pb ; This is because according to the central limit theorem which says the sampling distribution of sample means approaches a normal distribution as sample size gets larger irrespective if the shape of the Population distribution. Hence, the distribution of sample differences will follow a normal distribution and the mean will Hence be the difference in the population mean.