Answer to Question #187043 in Statistics and Probability for Samantha

Question

Average Senior High School annual cost of tuition fee for all private schools last year was 46,300 a random sample of costs this year for 45 private schools indicated that the sample mean was 47,800 and a sample standard deviation was 5600 at the 0.10 level of significance, is there sufficient evidence to conclude that the cost has increased?

Answer 1

$\mu = 46300 \\ n = 45 \\ \bar{X} = 47800 \\ \sigma = 5600 \\ z = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}} \\ z = \frac{47800 -46300}{5600 / \sqrt{45}} \\ = \frac{1500}{834.82} \\ = 1.79 \\ Z_{λ/2} = Z_{0.10/2} = Z_{0.05} = 1.645 \\ 1.79 > 1.645$

There is sufficient evidence to conclude that the cost has increased.