Question

The State Board of Education in Georgia is considering introducing a new initiative to boost the reading levels of fourth graders. The current population mean reading level of a fourth grader is 800 points. To assess the impact of the initiative, the developers were given permission to pilot their ideas in the classrooms of several area elementary schools. At the end of the pilot, a sample of 1000 fourth graders produced an average reading level of 856 points with a population standard deviation of 98. Using a 0.05 level of significance, test the claim the new initiative will increase the mean reading levels of fourth graders from 800 points.

Answer 1

21. Here claim is that $H_0:\mu=800$ vs $H_a:\mu>800$

So the test statistics is $z=\frac{\overline{x}-\mu}{\frac{\sigma }{\sqrt{n}}}=\frac{856-800}{\frac{98}{\sqrt{1000}}}=18.07$

Hence the P value is $P(z>18.07)=0.00000$