Respuesta :
Using the Central Limit Theorem, it is found that the sampling distribution will be approximately normal, with mean of -0.04 and standard error of 0.0423.
What does the Central Limit Theorem state?
- It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]
- It also states that when two variables are subtracted, the mean is the subtraction of the means, and the standard deviation is the square root of the sum of the variances.
In this problem, for each sample, the mean and the standard error are given by:
[tex]p_C = 0.08, s_C = \sqrt{\frac{0.08(0.92)}{100}} = 0.0271[/tex]
[tex]p_A = 0.12, s_A = \sqrt{\frac{0.12(0.88)}{100}} = 0.0325[/tex]
Then, for the distribution of differences, we have that:
[tex]p = p_C - p_A = 0.08 - 0.12 = -0.04[/tex]
[tex]s = \sqrt{s_C^2 + s_A^2} = \sqrt{0.0271^2 + 0.0325^2} = 0.0423[/tex]
The sampling distribution will be approximately normal, with mean of -0.04 and standard error of 0.0423.
To learn more about the Central Limit Theorem, you can check https://brainly.com/question/24663213
