Question

Average Senior High School annual cost of tuition fee for all private schools last year was Php43,700. A random sample of costs this year for 45 private schools indicated that the sample mean was Php45,800 and a sample standard deviation was Php5,600. At 0.01 level of significance, is there sufficient evidence to conclude that the cost increased?

Answer 1

$H_0:\mu \leqslant 43700\\H_1:\mu >43700\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{45}\frac{45800-43700}{5600}=2.51558\sim t_{n-1}=t_{44}\\P-value:\\P\left( T>2.51558 \right) =F_{t,44}\left( -2.51558 \right) =0.0078$

Since the P-value is less than the significance level, the mean value increased.