Question

"Your teacher brings two bags of colored goldfish crackers to class. Bag I has 25% red crackers and Bag II has 35% red crackers. Each bag contains more than 1000 crackers. Using a paper cup, your teacher takes an SRS of 50 crackers from Bag I and a separate SRS of 40 crackers from Bag II. Let p1-p2 be the difference in the sample proportions of red crackers. " The object is to find the standard deviation. I have 0. 971. Is this correct? I would like to verify

Answer 1

Using the Central Limit Theorem, it is found that the standard deviation is of 0.0971.

What does the Central Limit Theorem states?

• It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1 - p)}{n}}$, as long as $np \geq 10$ and $n(1 - p) \geq 10$.

• It also states that when two variables are subtracted, the standard deviation is the square root of the sum of the variances.

In this problem, for each sample, the standard error is given by:

$s_I = \sqrt{\frac{0.25(0.75)}{50}} = 0.0612$

$s_{II} = \sqrt{\frac{0.35(0.65)}{40}} = 0.0754$

Hence, for the distribution of differences, it is given by:

$s = \sqrt{s_I^2 + s_{II}^2} = \sqrt{0.0612^2 + 0.0754^2} = 0.0971$

More can be learned about the Central Limit Theorem at brainly.com/question/24663213