Suppose the ages of students in your program follow a positively skewed distribution with mean of 24 years and a standard deviation of 4 years.If we randomly sampled 100 students,which of the following statements about the sampling distribution of the sample mean age is NOT true?
A)The mean of the sampling distribution of sample mean is equal to 24 years.
B)The standard deviation of the sampling distribution of sample mean is equal to 4 years.
C)The shape of the sampling distribution of sample mean is approximately normal.
D)All of these choices are true.

Question

Quizplus · Accepted Answer

The standard deviation of the sampling distribution of sample mean is not equal to the standard deviation of the population, but rather the standard deviation of the population divided by the square root of the sample size. In this case, the standard deviation of the sampling distribution of sample mean would be 4/sqrt(100) = 0.4 years. Therefore, statement B is not true. Statements A and C are true because the mean of the sampling distribution of sample mean is always equal to the population mean, and the shape of the sampling distribution of sample mean is approximately normal due to the Central Limit Theorem.

Suppose the Ages of Students in Your Program Follow a Positively