Question

QUESTIONS You want to test which candy gets you the best ratings on student evaluations (0-10). The first set of students gets no candy, the second gets black licorice, and the third gets skittles. You test 4 people in each group No Black Candy Licorice Skittles 4 3 N - 12 3 4 G48 1 3 6 EX2 - 238 5 4 1 6 8 24 T- M- SS- 16 4 2 6 2 4 8 a. State the null hypothesis and alternative hypothesis, in both symbols and words. b. Calculate the appropriate ANOVA and fill in the ANOVA Summary table below. SS DF MS F Between Within Total c. What is the Ferit value you should be using to make your hypothesis testing decision at a- .052 Should you relect or falltrelert the nata052

Answer 1

Soin. Given, data No Candy Black Licorice 3 Skittles 8 3 4 s 3 N=12 G = 48 1 ZX2= 238 16 8 24 4 G S- २ 4 8 Now know TSS= Zx? 238:- (48)2 12 N V 157 case TSS = 238-192 = 46 with ef=N-1 = 13-1 = 11. and SSW = IE (Xij- X;)? where k=number of groups ..k3 in our ., SSW = Q+4 + 8 = 14 and dif. = N-K= 12-3 = 9 and SSB 을 Tie GP 162 २ 24? 548)2 32. Nj N 4 4 12 こ - + :ن where and dof. K-1 = 3-1 =3. TSS - Total sum of Square SSW Within. sum of Square SSB Between Sum of square @ Hypothesis Ho: li= ls = 13 Ha! li #ej for at least one 1 +j =1,2,3 OR in words Ho: Mean of all three groups is same, Ma: Mean of at least two groups. is not same. where li= mean of 1st group (No candy) Ma= mean of and group ( Black Licorice) ICS Scanned with CamScanner

ug mean of 3rd group skittles) ANOVA. Table: We fill out ANOVA table using calculations facom the begining of the answer SS OF MS ܢܐ 16 32 २ 10.28 104 14 9 1.5556 46 11 Between Within Total where, MS-SS DF 10.28 4 and E- MSB MSW 1.5556 .: MSB = 32 cis MSW = 14 -1.5556 9 २ 3 © We know for one-way ANOVA MSB a Fadfs, afa) Mew where do tevel of significance ofi = Between ss dif. df2= Within S.S. df this value Thus Fest Focos (2,3) in from case, we obtain E-table. Ecrit 4.26 O Notice that 10,28% 4.26 F> Fcrit le in this case there is strong evidence reject null hypothesis. hypothesis at 9=0.05 to Thus, We reject the null. @ Yes! , Since we rejected nw hypothesis means we accept the alternative hypothesis that at least two groups means are different Thus, candy have an effect on evaluation_scores CS Scanned with CamScanner