Question

Sample proportions List all $6$possible SRSS of size $n=2$, calculate the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dotplot. Is the sample proportion an unbiased estimator of the population proportion? Explain your answer.

COLOR	AGE
RED	$1$
WHITE	$5$
SILVER	$8$
RED	$20$

Short answer

The required dotplot isand sample proportion an unbiased estimator of the population proportion.

Step-by-step solution

Given information

We need to find out the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dotplot and whether the sample proportion is an unbiased estimator of the population proportion or not.

COLOR	AGE
RED	$1$
WHITE	$5$
SILVER	$8$
RED	$20$

Explanation

We know that

The sample proportion of all the red cars is equal to half of the no. of red cars in the sample.

Sample of size two	Number of red cars	Proportion of red cars
$1,2$	$1$	$0.5$
$1,3$	$1$	$0.5$
$1,4$	$1$	$0.5$
$2,3$	$0$	$0$
$2,4$	$1$	$0.5$
$3,4$	$2$	$1$

And the required dotplot is,

As the mean of sampling distribution is equal to population proportion.

So, the sample proportion an unbiased estimator of the population proportion.