Answer to Question #314376 in Statistics and Probability for Rahul

Question

study was made of a sample of 25 records of patients seen at a chronic

disease hospital on an

outpatient basis. The mean number of outpatient visits per patient was 4.8,

and the sample standard

deviation was 2. Can it be concluded from these data that the population mean

is greater than four

visits per patient? Let the probability of committing a type I error be .05. What

assumptions are

necessary?

Answer 1

$H_0:\mu \leqslant 4\\H_1:\mu >4\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{25}\frac{4.8-4}{2}=2\sim t_{n-1}=t_{24}\\P-value:\\P\left( T>2 \right) =F_{t,24}\left( -2 \right) =0.0285$

Since the P-value is greater than 0.05, the null hypothesis is declined. There is an evidence, that the population mean is greater than four visits per patient.