A high-school department made a change in its curriculum. One of the instructors in the department suspected that the change would result in a lowering of math skills. Students in the old program showed a mean of 70 points on a mathematics proficiency exam. Forty-two students from the new program had the scores in the dataset MATHEMATICS TEST SCORES (attached). The standard deviation of the all students over the years has been 10.34. Use a 2% level of significance.
a. Set up a hypothesis test
i. State the null and alternative hypothesis
ii. Confidence intervals of scores and the z or t intervals.
b. What are the results of the test (do the data indicate that the new program results in a lowering of math skills).
c. Do a P test. Are the two tests consistent?
d. Should the department us the new curriculum and why?