Degrees of freedom t.100 t.050 t.025 t.010 t.005 3.0777 6.3138 12.7062 31.8207 63.6574 2 1.8856 2.9200 4.3027 6.9646 9.9248 3 1.6377 2.3534 3.1824 4.5407 5.8409 4 1.5332 2.1318 2.7764 3.7469 4.6041 5 1.4759 2.0150 2.5706 3.3649 4.0322 6 1.4398 1.9432 2.4469 3.1427 3.7074 7 1.4149 1.8946 2.3646 2.9980 3.4995 8 1.3968 1.8595 2.3060 2.8965 3.3554 9 1.3830 1.8331 2.2622 2.8214 3.2498 10 1.3722 1.8125 2.2281 2.7638 3.1693 11 1.3634 1.7959 2.2010 2.7181 3.1058 12 1.3562 1.7823 2.1788 2.6810 3.0545 13 1.3502 1.7709 2.1604 2.6503 3.0123 14 1.3450 1.7613 2.1448 2.6245 2.9768 15 1.3406 1.7531 2.1315 2.6025 2.9467 16 1.3368 1.7459 2.1199 2.5835 2.9208 17 1.3334 1.7396 2.1098 2.5669 2.8982 18 1.3304 1.7341 2.1009 2.5524 2.8784 19 1.3277 1.7291 2.0930 2.5395 2.8609 20 1.3253 1.7247 2.0860 2.5280 2.8453 21 1.3232 1.7207 2.0796 2.5177 2.8314 22 1.3212 1.7171 2.0739 2.5083 2.8188Geoff is the proud owner of a restaurant. He is interested in determining whether his Wagyu beef or Hiramasa kingsh sasm'mi should be marketed as the Geoff Special. Geoff has selected a random sample of 20 people to taste his Wagyu beef and give it a score out of 100. He also selected a different random sample of 20 people to taste his Hiramasa kingsh sashi'mi' and give it a score out of 100. The sample mean score given to the Wagyu beef dish was calculated as 66.20. The sample standard deviation of the scores for the Wagyu beefdish was calculated as 3. The sample mean score given to the Hframasa kingsh sashi'mi dish was calculated as 71.6. The sample standard deviation of the scores for the Hiramasa kingsh sasm'mi' dish was calculated as 5. The population standard deviations of the scores for each dish are unknown, but Geoff believes that it is reasonable to assume that they are equal. You may nd this Student's t distribution table useful throughout the following questions. a) Geoff would like to test whether the mean scores of each of these dishes are equal. He has constructed a hypothesis test with H0: l'w = pH and HA: \"W a: u\". Calculate the test statistic (t) for this hypothesis test. Give your answer to 2 decimal places. b) Usmg the test statistic for Geoff's hypothesis test and a 913% condence level, Geoff should the null hypothesis. A studyr compared the individual preetax vearlyr income earned by residents from two states. The following table lists the statistics resulting from this study: Yearlyr Income Location Sample Size Sample Mean ($'0005) Sample Standard Deviation ($11005) State A 14 98 26 State B 28 45 30 A part of the studyr involved calculating the upper and lower bound of the 90% confidante interval of the mean difference (State A State ES) between the income earned by individuals from the two states. For the purposes of this study, it is assumed that the population standard deviations of the two populations are equal. Calculate the confidence interval. Give your answers to 2 decimal places. You may find this Student's t distribution table useful. a) Lower bound = E E b) Upper bound
