Q. 19 Sample proportions List all 6聽p... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 7: Q. 19 (page 456)

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

Expert verified

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.

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Car Number	Color	Age
$1$	Red	$1$
$2$	White	$5$
$3$	Silver	$8$
$4$	Red	$20$

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