Question

A sample of n = 25 scores is selected from a population with m = 50 and s = 10. The probability of obtaining a sample mean greater than 55 is p = 0.3085. True or False?

Answer 1

The statement 'the probability of obtaining a sample mean greater than 55 is p = 0.3085' is false.

Step-by-step explanation:

To determine if the statement is true or false, we need to calculate the z-score and compare it to the p-value given.

Given: n = 25, μ = 50, s = 10, p = 0.3085

First, we calculate the standard error of the mean (SE):

SE = s / sqrt(n) = 10 / sqrt(25) = 10 / 5 = 2

Next, we calculate the z-score:

z = (sample mean - population mean) / SE = (55 - 50) / 2 = 5 / 2 = 2.5

Using a standard normal distribution table or calculator, we find that the probability of obtaining a z-score greater than 2.5 is approximately 0.0062.

Since 0.0062 is less than 0.3085, which is the given probability, the statement 'the probability of obtaining a sample mean greater than 55 is p = 0.3085' is false.