Answer to Question #314705 in Statistics and Probability for rainyyyyy

Question

Perform the hypothesis of the following scenarios.

The graduate record exam is standardized test recquired to be admitted to many graduate schools in the United States. A high score in GRE makes admissions more likely. According th the educational testing service, the mean score for takers of GRE who do not have training courses is 555 with standard deviation of 139. Brain Philippine offers expensive GRE training courses, claiming their graduates score better than those who have not talen any training courses. To test the company's claim, a statisticiam randomly selected 30 graduates of BP and asked their GRE scores. They recorded a mean score of 560 in GRE. Is the company's claim true, using a 95% confidence level?

Answer 1

$H_0:\mu =555\\H_1:\mu >555\\\sigma =139\\n=30\\\bar{x}=560\\Z=\sqrt{n}\frac{\bar{x}-\mu}{\sigma}=\sqrt{30}\frac{560-555}{139}=0.197023\sim N\left( 0,1 \right) \\P-value:\\P\left( Z>0.137023 \right) =\varPhi \left( -0.137023 \right) =0.4455\\$

The P-value is greater than $\alpha=0.05$ , hence there is no evidence that training is effective.