Question

4. Use the Rank-Sum Test comparing prices of Red Sox and White Sox tickets. Red Sox 12 14 17 12 20 25 25 20 18 16 White Sox 10 8 14 22 19 8 11 17 a) Suate the Null Hypothesis: a) b) Compute the test statistic: J b) c) Compute the value c) 5. A dle was rolled 90 times. The results were: OBserved # Frequency 1 20 2 22 3 10 4 8 5 13 6 17 Find the test- statistic that would be used to determine whether the die is a poodness of fit or is loaded. 6. Using the Chi-Square test to determine whether class in college is independent of favorite type of movie, given data: Comedy SCI-FI 13 65 90 90 14th 75 75 15 80 80 16° 65 a) Find the expected values. (put next to Observed) b) Find the test statistic.

Answer 1

Solutions Z Z Given that Sample value Rank Rank (Adjusted roo hy). 8 lo 106 2 10 3 u 3 и Boog ---- 5 12 12 5o5 5.5 705 9. 1น lu 16 17 17 18 lo 11 10.5 10.3 12 19 13 iu ----89-R 13 16 17 18 14.5 1400 16 170 17-5 © The sum of Ranko Foo sample i io R-6.5+ 5•7+75+9+103712+ 14057146371700771760 R = llu and The sum of Ranko of sample a io Ra= logt 105+3+ 4+75 + 10.5 +13+16 R2 57 Hence. The list stabiotic R=R,= 114. a TO Test Ho: Median (Diffeecoce) - 0 HA : Median (Diffcoence) #0

C en given that This cooleg ponds to a Chi-guerre test for Croodncoo of fit. © p-value <0.00 A dile was solled Go timeo Ho : The dice is faio i.eu poopoolion of each no-5 Ho ? come of the population poopooliono diffico room the values stated in the mall hypothesis. olepi :- step2;. Test Statico Dalal obocrved Eapected poopoolioro Expected Values dia. (Fo-fe) 35c values cro) 20 0016 15.00 1•667 2 0:161 15.00 3.267 3 10 0.167 15.00 10662 u oo 0.167 -16.00 3.267 5 13 0:167 15.00 0.267 17 0:16 7 15.00 -0.267 6 Total 90 1.000 90.00 100400 2 a 100400 Step 3: Z Z df = 6-1=5 As the level of segnificance so not ghen, we will take alpha -0.05. x costical = 110 070 AJ x*10:40) 80 less than tu coitical, ut fail to object The null ypothesis. Hence at alpah = 0.08. Le do not have Gufficient Evidence to believe that the dice is loaded. *

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