Question

Conduct P-value method

The Mathematics Department in a certain university is conducting a study to determine how long it takes its graduates to find a job. A sample of 80 graduates was surveyed and it was found out that the average time it has taken a graduate to find a new job is 2.5 months, with a standard deviation of 2 months. Is there a sufficient evidence to conclude that the graduate of this department takes on the average more than two months to find a job? Use the 90% confidence level. 

Answer 1

$H_0:\mu \leqslant 2\\H_1:\mu >2\\n=80\\\bar{x}=2.5\\s=2\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{80}\frac{2.5-2}{2}=2.23607\sim t_{n-1}=t_{79}\\P-value:\\P\left( T>2.23607 \right) =F_{t,79}\left( -2.23607 \right) =0.014\\$