Question

Sample minimums List all $6$possible SRSS of size $n=2$, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dotplot. Is the sample minimum an unbiased estimator of the population minimum? Explain your answer.

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

Short answer

The required dotplot is and sample proportion not an unbiased estimator of the population proportion.

Step-by-step solution

Given information

We need to find out the proportion of cars in the sample, 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	Sample minimum
$1,2$	$1$
$1,3$	$1$
$1,4$	$1$
$2,3$	$5$
$2,4$	$5$
$3,4$	$8$

And the required dotplot is,

As the mean of sampling distribution is not equal to population proportion.

So, the sample proportion not an unbiased estimator of the population proportion.