Please show formula used and for testing hypotheses question be sure to show all steps: null and alternative hypotheses, test statistics, rejection region, computation of test statistic, and conclusion. Thanks.

Q1 (10.2.5 in 7th Ed.) 10-19. Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1. re- sulting in an average yield of 86 and a sample standard devia- tion of 3. Fifteen batches were prepared using catalyst 2. and they resulted in an average yield of 89 with a standard devia- tion of 2. Assume that yield measurements are approximately normally distributed with the same standard deviation. (a) Is there evidence to support a claim that catalyst 2 pro- duces a higher mean yield than catalyst 12' Use or = 0.0 l. (b) Find a 95% condence interval on the difference in mean yields. (12 (10.2.6 in 7th Ed.) 1022. Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is an important characteristic. A random sample of [0 gears from supplier ] results in f1 = 290 and 51 = 12. while another random sample of 16 gears from the second supplier results in 32 = 321 and 52 = 22. (a) ls there evidence to support the claim that supplier 2 pro- vides gears with higher mean impact strength? Use or = 0.05, and assume that both populations are normally dis- tributed but the variances are not equal. (b) What is the P-value for this test? (c) Do the data support the claim that the mean impact strength of gears from supplier 2 is at least 25 foot-pounds higher than that of supplier 1? Make the same assump- Q3. 10.4.2 in '7tll Ed. 1038. A computer scientist is investigating the usefulness of two different design languages in improving programming tasks. Twelve expert programmers. familiar with both lan- guages. are asked to code a standard function in both lan- guages. and the time 1 in minutes) is recorded. The data follow: Time Design Design Language Language Programmer 1 2 1 1? 18 2 16 14 3 21 19 4 l4 1 l 5 18 23 6 24 21 7 16 10 8 14 13 9 21 19 10 23 24 1 1 13 15 12 18 20 (a) Find a 95% condence interval on the difference in mean coding times. 15 there any indication that one design lan- guage is preferable? (b) Is the assumption that the difference in coding time is nor- mally distributed reasonable? Show evidence to support your answer. (14. (10.5.2 in 7... Ed.) 10-47. Two chemical companies can supply a raw material. The concentration of a particular element in this material is important. The mean concentration for both suppliers is the same, but we suspect that the variability in concentration may differ between the two companies. The standard deviation of concentration in a random sample of In = 10 batches pro- duced by company 1 is 51 = 4.7 grams per liter. while for company 2. a random sample of :22 = 16 batches yields 32 = 5.8 grams per liter. Is there sufcient evidence to conclude that the two population variances differ? Use or = 0.05. Q5. (10.6.4 in 7'\" Ed.) 1065. A random sample of 500 adult residents of Maricopa County found that 385 were in favor of increasing the high- way speed limit to 75 mph. while another sample of 400 adult residents of Pima County found that 267 were in favor of the increased speed limit. Do these data indicate that there is a dif- ference in the support for increasing the speed limit between the residents of the two counties\"? Use or = 0.05. What is the Pvalue for this test