Question

Algebra scores in a school district are normally distributed with a mean of 74 and standard deviation 6. A new teaching-and-learning system, intended to increase average scores, is introduced to a random sample of 30 students, and in the first year the average was 76.

(a) What is the probability that an average as high as 76 would have been obtained under the old system?

(b) What is the null hypothesis for testing the new system, and what is the alternative hypothesis?

(c) Is the test significant at the 0.05 level? What about the 0.01 level? Explain your answers.

Answer 1

Ans:

a)

z=(76-74)/(6/sqrt(30))

z=1.826

P(z>1.826)=0.0339

b)

c)p-value=0.0339

As,p-value<0.05,so we reject the null hypothesis and results are significant at alpha=0.05

As,p-value>0.01,so we fail to reject the null hypothesis and results are not significant at alpha=0.01