Answer:
[tex] \hat p = \frac{\sum_{i=1}^{40} \hat p_i}{40}[/tex]
[tex] \hat p = 0.493[/tex]
And the deviation is given by this formula:
[tex] s_{\hat p}= \frac{\sum_{i=1}^{40} (\hat p_i - \hat p)^2}{n-1}= 0.085[/tex]
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 :
[tex] \% Error = \frac{0.5-0.493}{0.5}* 100 = 1.4\%[/tex]
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:
[tex] \hat p = \frac{\sum_{i=1}^{40} \hat p_i}{40}[/tex]
[tex] \hat p = 0.493[/tex]
And the deviation is given by this formula:
[tex] s_{\hat p}= \frac{\sum_{i=1}^{40} (\hat p_i - \hat p)^2}{n-1}= 0.085[/tex]
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 :
[tex] \% Error = \frac{0.5-0.493}{0.5}* 100 = 1.4\%[/tex]
