1. An IQ test given to two different groups of high school students produces the following results: group 1 of size 40 has a mean of 112 with a standard deviation of 6 and group 2 of size 60 has a mean of 114 with a standard deviation of 4. Test the null hypothesis of no mean difference against both the one-sided and two-sided alternative hypotheses and report the results as a P-value. At what level of significance can the null hypothesis be rejected?

2.Dr. Frost is a researcher in a large school district that annually evaluates their students academic progress in mathematics using the Iowa Test of Basic Skills (ITBS). In the testing manual for the ITBS she discovers that the average performance of sixth-grade students in the nation on this test is 85 and that the standard deviation of scores in the nation is 20. She wants to know if students in her school district are performing at the same level. How could she go about testing this? What if the standard deviation of scores in the nation were 30? What if it was 10? Use = 0.01.

-state your null

-alternative hypotheses

-the type of test,

-the P-Value,

( the required test using the P-Value approach, whether you reject the null or do not reject, )

-the conclusion in the context of the problem.