Answer to Question #318010 in Statistics and Probability for Yharim

Question

The average pre-school cost for tuition fees last year was Php. 17,250. The following year 20 institutions had a sample mean of Php. 16,150 and a standard deviation of Php. 2,250. At 0.90 level of confidence is there sufficient evidence to conclude that the mean cost has increased?

Answer 1

$H_0:\mu =17250\\H_1:\mu >17250\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{20}\frac{16150-17250}{2250}=-2.18638\sim t_{n-1}=t_{19}\\P-value:\\P\left( T>-2.18638 \right) =F_{t,19}\left( 2.18638 \right) =0.979$

Since the P-value is greater than the significance level, the mean value has not increased.