Answer to Question #314434 in Statistics and Probability for Rahul

Question

A sample of 25 freshman nursing students made a mean score of 77 on a

test designed to measure

attitude toward the dying patient. The sample standard deviation was 10. Do

these data provide

sufficient evidence to indicate, at the .05 level of significance, that the

population mean is less than

80? What assumptions are necessary?

Answer 1

$H_0:\mu \geqslant 80\\H_1:\mu <80\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{25}\frac{77-80}{10}=-1.5\sim t_{n-1}=t_{24}\\P-value:\\P\left( T<-1.5 \right) =F_{t,24}\left( -1.5 \right) =0.0733$

Since the P-value exceeds the significance level, there is not enough evidence that the mean value is less than 80.

The assumption is normality.