Question

A survey of 100 similar-sized hospitals revealed a mean daily census in

the pediatrics service of 27

with a standard deviation of 6.5. Do these data provide sufficient evidence to

indicate that the

1. population mean is greater than 25? Let alpha = 0.5

Answer 1

$H_0:\mu \leqslant 25\\H_1:\mu >25\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{100}\frac{27-25}{6.5}=3.07692\sim t_{n-1}=t_{99}\\P-value:\\P\left( T>3.07692 \right) =F_{t,99}\left( -3.07692 \right) =0.00135$

Since the P-value is less than the significance level, the population mean is greater than 25.