A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.What is the probability of selecting a sample mean of 13 or larger from this population?
A) equal to the probability of selecting a score above the mean
B) about one standard deviation below the mean
C) less than .10
D) greater than .31

Question

Quizplus · Accepted Answer

To find the probability of selecting a sample mean of 13 or larger, we use the formula for the standard error of the mean (SEM = σ/√n), where σ is the population standard deviation and n is the sample size. Here, SEM = 3.5/√49 = 0.5. The Z-score for a sample mean of 13 is (13 - 12)/0.5 = 2. A Z-score of 2 corresponds to a probability of less than .10 in the upper tail of the normal distribution, indicating that the probability of selecting a sample mean of 13 or larger is less than .10.

A Researcher Selects a Sample of 49 Participants from a Population