1. In a large American university in 1969, the male and female professors were sampled independently, yielding the following annual salaries (in thousands of dollars): Male Female 12 9 11 12 19 8 16 10 22 16 Test if there was a wage discrimination against women. Assume 1% level of significance. (Please specify the null and alternative hypotheses carefully) 2. 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: Breaking Temperature New Old 475 485 436 438 495 493 483 486 426 433 Does the new process shows significant improvement over the old process? Assume 5% significance level. (Please specify the null and alternative hypotheses carefully) . 3. To see what difference class attendance made, a professor sampled grades from his large statistics class of 530 students. From the 220 students who attended class less than half the time (the \"irregulars\"), he took a random sample of 5 grades. From the remaining 310 students who attended at least half the time (the \"regulars\"), he took an independent random sample of 5 other grades: Irregulars Regulars 41 69 81 56 52 83 69 70 62 92 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. A sample survey to estimate the fast-food market in a large city was kept small enough to allow repeated follow-up. The high response rate meant that the sample was essentially random. The survey recorded the number of fast-food meals eaten by each person in the previous 7 days, and to summarize: : the sample average is 0.82; s = 0.48; n=180. Calculate a 95% confidence interval for the mean of the whole population of this city. You may assume a two-tailed test. .