Question

could someone please help me solve this and show the steps on the calculator?? thank you!!

8. The contingency (two-way) table below shows the results of a random sample of 2197 adults classified by their favorite way to eat ice cream and gender. Gender Cone Sundae Sandwich Other Total Male 504 287 182 43 53 1069 Female 474 401 158 45 50 1128 Total 978 688 340 88 103 2197 Cup At alpha 01, can you conclude that one's favorite way to eat ice cream and one's gender are related? Ha gender and ice cream preference are independent

Answer 1

table results 0 their favourite way uandom to eat ice-cream and 504 a87 102 43 53 2069 444 401 158 45 IL22 948 688 3५० 88 L03 2197 to A contingency showing sample 0194 adults classified genden. Gendeu Cup Cone Sundae sandwich Other Total Male Female Total le find: - 44 alpha = 0.01, conclude that the rouiables fawowile way eat ice-cream and gender fisst of all, astume that the amiables forumile way to eat fee - cheam and gendeu independent flow, we will calculate the ma expected frequency fow each cell in the contingency table. Expected frequency Ex,e = lsum of now u). (sum of columns) The expected frequencies for E1, 1 = to 69x 970 445.862, EL alle uelated. alle Sample size the first now alle :- 1069 x 698 334.762 2197 2147 1069x88 2197 w 42.018 10 69x340 165.435 2197 EL, 5= 1069x 103 50.117 2147 The expected frequencies for the second now are :- EL = 1109x 970 X 50 2. 132 2197 F2,3 = 1128x340 ~ 174.565 2147 Edd - 1128x688 ~ 553. 139 2147 E2,4 = 11.28 x 88 – 45.182 2197 52.893 = 11 20 x 103 197

test whether the raniables are que to eat ice cream and mandomly seleeted felice each eppested frequency sis at leasts and the adult wete we can use chin square independence test to independent, He: the ramiables favowite way to eat ine cream and gender independent. Ha : The rouiables favourite way gender dependent! The given cordingency table hos luoss and 5 columns. so, chi-square dif. = (4-1) (0-1) = (-1)(5-1) = 4 Because dequee of fueedom = 4 and = 0.01, the cuilical walue is Yö = 13.2270 the sejection segion is x?> 17.227. que The chi-square test statistic is shown below:- 0 E (0-E² (0-E)² 504 475.860 28.132 834.762-47762 204 791.4094241.66 30 86032 2.201.208644 6.81441933L 274.399225 1.658652794 182 165.435 16.565 43 0.033124 0.0007736 0.182 42.018 50.117 53 $174 401 158 45 2. 083 2.311609 0.165045701 502.132 -20.132 191.4094241.546098365 353.23047.762 2201.208644 6.457993319 L74.565 -16.565 274.399225 1.571902973 -0.192 0.033124 0.000733124 52.893 - 2.883 0.311689 0.157171204 x=3(0-5) 20.067 45.182 Бо E

The test Static. shows the location and chi. of the rejection region chi-square pince, ger 20.067 is in the rejection suegion, - Rejection region null hypothesis ees is rejected. x=0.0L 5 15 25 from the figure, x2 = 13. 227 X =20,067 we see that there is evidence at 1% level to eat ice-cream enough of significante to conclude that favourite way genden dependent. ale