MATH SOLVE

2 months ago

Q:
# Determine whether the statement is true or false. If it is false, rewrite it as a true statement. As the size of a sample increases, the standard deviation of the distribution of sample means increases. A. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means does not change." B. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means decreases." C. This statement is true. D. This statement is false. A true statement is, "As the size of a sample decreases, the standard deviation of the distribution of sample means decreases."

Accepted Solution

A:

Answer:B. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means decreasesStep-by-step explanation:Standard deviation of distribution of sample means = [tex]\sigma_{m}[/tex]Sample size = nPopulation standard deviation = [tex]\sigma[/tex]The formula to calculate the standard deviation of distribution of sample means is:[tex]\sigma_{m}=\frac{\sigma}{\sqrt{n}}[/tex]From the above relation we can see that:Standard deviation of the distribution of sample means is inversely related to the sample size. In inverse relation if one quantity increases the other will decrease. So, if the size of the sample is increased, the standard deviation of the distribution of sample means will Decrease.Hence, the given statement is False. Therefore, the correct answer will be:B. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means decreases"