Algebra scores in a school district are normally distributedwith a mean of 74 and standard deviation 6. A newteaching-and-learning system, intended to increase average scores,is introduced to a random sample of 30 students, and in the firstyear the average was 76.
(a) What is the probability that an average as high as 76 wouldhave been obtained under the old system?
(b) What is the null hypothesis for testing the new system, andwhat is the alternative hypothesis?
(c) Is the test significant at the 0.05 level? What about the0.01 level? Explain your answers.
