Question

For two populations of rabbits, R and S, the proportions of rabbits with white markings on their fur are given as pR and pS, respectively. Suppose that independent random samples of 50 rabbits from R and 100 rabbits from S are selected. Let pˆR be the sample proportion of rabbits with white markings from R, and let pˆS be the sample proportion of rabbits with white markings from S. What is the standard deviation of the sampling distribution of pˆR−pˆS ?

Answer 1

Answer:

The standard deviation is  $\hat p_{R} -\hat p_{S} = \sqrt{\frac{\hat p_{R}(1-\hat p_{R})}{50} + \frac{\hat p_{S}(1-\hat p_{S})}{100} }$

Step-by-step explanation:

The standard deviation of a sampling distribution is the standard error or a valuation of the standard deviation. Where statistic parameter is the mean it is referred to as the standard error of the mean.

The formula for standard deviation of a sampling distribution is as follows;

$\hat p_{R} -\hat p_{S} = \sqrt{\frac{\hat p_{R}(1-\hat p_{R})}{n_R} + \frac{\hat p_{S}(1-\hat p_{S})}{n_S} }$

Where;

${\hat p_{R}}$ = Sample proportion of rabbits with white markings from R

${\hat p_{S}}$ = Sample proportion of rabbits with white markings from S

$n_R$ = Number of from R = 50

$n_S$ = Number of from S = 100

Therefore, the standard deviation of the sampling distribution is given as follows;

$\hat p_{R} -\hat p_{S} = \sqrt{\frac{\hat p_{R}(1-\hat p_{R})}{50} + \frac{\hat p_{S}(1-\hat p_{S})}{100} }$.