Answer to Question #146640 in Statistics and Probability for Azlan

Question

A job placement director claims that the average starting salary for nurses is $24,000. A sample of 10 nurses has a mean of $23,450 and a standard deviation of $400. Is there enough evidence to reject the director’s claim at α = 0.05?

Answer 1

Null hypothesis H₀: μ = 24000 (claim)

Alternative hypotheses H₁: μ ≠ 24000

Since α = 0.05 and the test is a two-tailed test, the critical values are

t = -2.262 and 2.262

d.f. = 9

$t = \frac{23400 - 24000}{\frac{400}{\sqrt{10}}} = -4.35$

Reject the null hypotheses, because -4.35 < -2.262

There is enough evidence to reject the claim that the starting salary of nurses is $24000.