Geoff is the proud owner of a restaurant. He is interested in determining whether his Wagyu beef or Hiramasa kl'ngsh sashr'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 mo. He also selected a cifferent random sample of 20 people to taste his Hiramsa kingsh sashiml and give it a score out of 100. The sample mean score given to the Wagyu beef dish was calculated as 38.18. The sample standard deviation of the scores for the Wagyu beef dish was calculated as 3. The sample mean score given to the Hiramasa kl'ngsh sashimi dish was calculated as 73.37. The sample standard deviation of the scores for the Hiramsa kingsh sashiml' dish was calculated as 4. The population standard deviations of the scores for each dish are unknown. You may nd this Student's t dis'o'ibutjon table useful throughout the following questions. Note that Geoff always aims to use the easiest possible calculations, and so when using a two-sample ttest he will use the simplied formula for degrees of freedom whenever possible. a) Geoff would like to test whether the mean scores of each ofthese dishes are equal. He has constructed a hypothesis test with H0: l-lw = u\" and HA: l-lw as im- Calculate the test statistic (t) for this hypothesis test. Give your answer to 2 decimal places. b) Using the test statistic for Geoff's hypothesis test and a 90% condence level, Geoff should the null hypothesis. A study com pa red the individual pretax yearly income earned by residents from two states. The following table lists the statistics resulting from this study: Yearly Income Location Sample Size Sample Mean {$'Ds) Sample Standard Deviation {$'DDDS) State A 51 75 1.8 State B 56 60 2? A part of the study involved calculating the upper and lower bound of the 95% condence interval ofthe mean difference (State A State B) between the income earned by individuals from the two states. For the purposes of this study, the simplied forumla for the number of degrees offreedom in the appropriate tdistn'hution will be used. Calculate the condence interval. Give your answers to 2 decimal places. You may nd this Student's t distribution table useful. IJ) Upper bound = a) Lower bound = \\:| E