Question

Your teacher will report the mean and standard deviation of the sampling distribution created by the class.

Answer 1

Answer:

$\hat p = \frac{\sum_{i=1}^{40} \hat p_i}{40}$

$\hat p = 0.493$

And the deviation is given by this formula:

$s_{\hat p}= \frac{\sum_{i=1}^{40} (\hat p_i - \hat p)^2}{n-1}= 0.085$

And as we can see the population proportion expected for the number of heads 0.5  is very close to the mean of the sampling distribution, the error is :

$\% Error = \frac{0.5-0.493}{0.5}* 100 = 1.4\%$

Step-by-step explanation:

Assuming the data on the figure attached. We ar assuming that this is a sampling distribution of sample proportions of heads in 40 flips of a coin.

As we can see we have the following values:

0.25, 0.35, 0.375,0.375, 0.40,0.40,0.40, 0.425,0.425,0.425, 0.45,0.45,0.45,0.45, 0.475,0.475,0.475, 0.475,0.475, 0.50,0.50,0.50, 0.525,0.525,0.525,0.525, 0.55,0.55,0.55,0.55,0.55, 0.575,0.575,0.575 0.575, 0.575, 0.60,0.60, 0.65,0.65

And we can calculate the sample proportion with the following formula:

$\hat p = \frac{\sum_{i=1}^{40} \hat p_i}{40}$

$\hat p = 0.493$

And the deviation is given by this formula:

$s_{\hat p}= \frac{\sum_{i=1}^{40} (\hat p_i - \hat p)^2}{n-1}= 0.085$

And as we can see the population proportion expected for the number of heads 0.5  is very close to the mean of the sampling distribution, the error is :

$\% Error = \frac{0.5-0.493}{0.5}* 100 = 1.4\%$