Answer to Question #311971 in Statistics and Probability for hshshhshs

Question

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

Answer 1

Null hypothesis H₀: $\mu=17250$

Alternative hypothesis H_a: $\mu>17250$

Sample size $n=20$

Sample mean $\bar X=16150$

Sample standard deviation $\sigma =2250$

Significance level $\alpha=0.10$

Since the alternative hypothesis is that $\mu$ is greater than this is a right tailed hypothesis test.

Since the sample size is less than 30, we use the T test

$df=n-1=20-1=19$

Since $\alpha=0.10$ $T=1.328$

$t_c=\dfrac{\bar X-\mu_0}{S/\sqrt n}$ $=\dfrac{16150-17250}{2250/\sqrt {20}}$

$t_c=-2.186$

Since $t_c<T$ we reject the hypothesis.

Since the null hypothesis is rejected, there is sufficient evidence to conclude that the population mean cost has increased at 0.10 level of significance.