A recent report by the American Medical Association stated the average annual salary of psychiatrists is $189,121 with a population standard deviation of $26,975. A group of
Hospital administrators randomly sampled 64 psychiatrists and found an average annual
Salary of $198,630. The group claims that the average annual salary is actually higher
Than what the American Medical Association reported. What is the P-value for this
One-sided test?
A) 0.0035
B) 0.0024
C) 0.1328
D) 0.0237

Question

Quizplus · Accepted Answer

The P-value for a one-sided test can be calculated using the Z-score formula: Z = (X̄ - μ) / (σ/√n), where X̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the given values: Z = (198630 - 189121) / (26975/√64) = 3.53. Looking up the Z-score of 3.53 in the Z-table gives a P-value less than 0.0024 for a one-sided test, indicating strong evidence against the null hypothesis and supporting the claim that the average salary is higher.

A Recent Report by the American Medical Association Stated the Average