Answer to Question #327475 in Statistics and Probability for kleve

Question

Direction: Answer the given problem.

The Guidance Counselor of your school claims that the Grade 11 students spend an average of 11.28 hours in a week doing performance tasks with standard deviation of 1.64. Your adviser thinks that students spend more time in doing performance tasks, so he decided to conduct his own research. He used a sample of 46 Grade 11 students and obtained a mean of 11.83. Is there enough evidence at 0.05 level of significance that the students spend 11.28 hours in a week doing performance tasks?

Answer 1

$H_0:\mu =11.28\\H_1:\mu >11.28\\Z=\sqrt{n}\frac{\bar{x}-\mu}{\sigma}=\sqrt{46}\frac{11.83-11.28}{1.64}=2.27456\sim N\left( 0,1 \right) \\P\left( \left| Z \right|>2.27456 \right) =2\varPhi \left( -2.27456 \right) =2\cdot 0.0115=0.023<0.05\Rightarrow \\\Rightarrow H_0\,\,rejected, \mu >11.28$