Question

22% of high school students in the United Kingdom say that Dobby is their favoite character in the Harry Potter books. Let's assume this is the parameter value for the entire population of high school students in the U.K. You take a sample of 150 high school students and record the porportion, (p-hat) of individuals in your sample who say Dobby is their favorite character. a) What are the mean and Standard deviation of the sampling distribution of p-hat

Answer 1

Answer:

The mean of the sampling distribution is 0.22 and the standard deviation is 0.0338.

Step-by-step explanation:

Central Limit Theorem:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

In this question, we have that:

$p = 0.22, n = 150$

a) What are the mean and Standard deviation of the sampling distribution of p-hat

By the Central Limit Theorem,

Mean:

$\mu = p = 0.22$

Standard deviation:

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.22*0.78}{150}} = 0.0338$

The mean of the sampling distribution is 0.22 and the standard deviation is 0.0338.