Answer :
Answer:
D.) I would expect the means and standard deviations in the two test to be about the same, but the standard error in Test B should be smaller than in Test A.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
By the Central Limit Theorem:
Both tests, A and B, are of the same quantity, so they have the same mean and standard deviation. However, since the standard error is inversely proportional to the sample size, and test B has a greater sample size than test A, the standard error in test B should be lower, and thus, the correct answer is given by option D.