4 stats question

1. A firm producing plate glass has developed a less expensive tempering process to allow for fireplaces to rise to a higher temperature without breaking. To test it, five different plates of glass were drawn randomly from a production run, then cut in half, with one-half tempered by the new process, and the other half by the old. The two halves then were heated until they broke, yielding the following data:

Does the new process shows significant improvement over the old process? Assume 5% significance level. (Please specify the null and alternative hypotheses carefully)

2. In a large American university in 1969, the male and female professors were sample independently, yielding the following annual salaries (in thousand of dollars):

Test if there was wage inequality using the following methods: Assume 5% level of significance.

1. ANOVA
2. Two population t-test.
3. Are the two methods yield different conclusion? Why or Why not?

3. To see what difference class attendance made, a professor sampled grades from his large statistics class of 550 students. From the 230 students who attended class less than half the time (the “irregulars”), he took a random sample of 5 grades. From the remaining 320 students who attended at least half the time (the “regulars”), he took an independent random sample of 5 other grades:

Does the data support the contention that “it is worth 13 marks to come to class regularly? Assume 5% level of significance.(Please specify the null and alternative hypotheses carefully).

4. Why the F-distribution is positively skewed? Explain.