Question

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1) Danny LOVES watching his Warriors & Sharks play, but watching 82 games x 2 teams can take away a lot of his free time! Suppose he is interested in whether Warriors or Sharks games are longer, so he takes a random sample of each team's games and records the games lengths. Conduct a test at the 5% level to determine if the average length of a Warriors game is different from that of a Sharks game. Warriors: sample average length = 126 minutes, population standard deviation 11 minutes; sample size 30 Sharks: sample average length 138 minutes, population a) State the null & alternative hypotheses, in the context of the problem. b) Describe the type I & type II errors in the context of the problem. c) Describe the sample statistic in the context of the problem. Find its distribution & explain why. d) Use your TI to find the p-value, sketch the region whose area the probability represents (label the appropriate values along the horizontal axis), and define the p-value in the context of the problem. e) Make your conclusion in the context of the problem. Explain why. standard deviation 24 minutes; sample size = 40

Answer 1

Xai length ob ith game of wovious -1(4) ng =30 1-1 (4) n2=40 KIX Xai N(4, 1)XaiN(,2 th Shwr hs a) Ho 2 Conclu dling avg length dibbers when Ahey 6) Tyhe I enon acfually the same ane Concluding avg length does not dillen when they Ty he enor actually dilleret ane (6 --)(0, 4) 41 _ N 2 (A4 2 Text Sttintie Given X= 426 X2138 x-X 2412 N (0,1) tHo AL12 Z2.794 -- P-Value- P 2 r0,4)- A Volue P(Flsely concluding 0.002 avenage fime oh loth dea m's game aesinmitart not imila hen they ane actually enual pvalue vclue 0.05 -9.794 Ho at level 0.05,a of two teams e) Reject Conclusion Avg gane longths, dillers om one another