Question

The average preschool cost for tuition fees last year was 17,250. The following year, 20 institutions had a mean of 16,150 and a standard deviation of 2,250 is there sufficient evidence at =0.10 level of significance to conclude that the mean cost has increased?

Answer 1

We have:

$H_0:\mu =17250\\H_1:\mu >17250$

The statistic is

$T=\sqrt{n}\frac{\bar{x}-17250}{s}\sim t_{n-1},\\T=\sqrt{20}\frac{16150-17250}{2250}=-2.18638.$

The P-value is

$P\left( T>-2.18638 \right) =F_{T,19}\left( 2.18638 \right) =0.979$

Since the P-value is greater than the significance level, the null hypothesis is not declined. The mean cost has not increased.