Question

Your friend likes to show off to his coworkers using statistical terminology, but he makes errors so much that you often have to correct him. He just completed the following hypothesis test: H0 : μ = 100 ; HA : μ ≠ 100 x = 105, s = 10, n = 40 p-value = 0.0016 He claims the definition of this p-value is "the probability of obtaining a sample mean of 105 from a random sample of n = 40 when the true population mean is assumed to be 100." Which of the following is true?

a. Your friend is wrong, the sample size is irrelevant.
b. Your friend is right.
c. Your friend is wrong, the statement should be revised as "the probability of obtaining a sample mean of 105 from a random sample of n = 40 when the true population mean is assumed to be different than 105."
d. Your friend is wrong, the statement should be revised as "the probability of obtaining a sample mean of 105 or more extreme from a random sample of n = 40 when the true population mean is assumed to be 100."

Answer 1

Option d: Your friend is wrong, the statement should be revised as "the probability of obtaining a sample mean of 105 or more extreme from a random sample of n = 40 when the true population mean is assumed to be 100."

Explanation:

We are given;

Null hypothesis; H0 : μ = 100

Alternative hypothesis; HA : μ ≠ 100

Sample mean; x = 105

Sample standard deviation; s = 10

Sample size; n = 40

p - value = 0.0016

Looking at the options, the first option is wrong because the sample size is not irrelevant her since it's more than 30.

The second option can't be correct because they just told us he is right without giving explanation.

The third option is wrong because 100 is the true population mean and not 150.

Thus we are left with Option D as the correct answer.