A recent report from the American Medical Association claims that for the first time in 10 years, the average salary of psychiatrists was $189,121 with a standard deviation of $26,975. A random sample
Of 25 Canadian psychiatrists this year yielded an average salary of $198,630. Is there evidence that the
Average salary is actually higher than what the American Medical Association reported (assume that the
Variation in Canadian salaries is the same as that in the US)? What is the p-value for a one-sided test?
A) 0.0024
B) 0.0035
C) 0.1328
D) 0.0390

Question

Quizplus · Accepted Answer

We need to conduct a one-sided hypothesis test with the null hypothesis being that the average salary is equal to $189,121 and the alternative hypothesis being that the average salary is greater than $189,121. Assuming a normal distribution, we can calculate the test statistic as:

t = (198630 - 189121) / (26975 / sqrt(25)) = 3.12

Using a t-distribution table with 24 degrees of freedom and a significance level of 0.05, the critical value is 1.711. Since our test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence that the average salary is higher than what the American Medical Association reported. The p-value for this one-sided test is the probability of observing a t-value greater than 3.12, which is approximately 0.0390. Therefore, the correct answer is D.

A Recent Report from the American Medical Association Claims That