Question

A 2010 study examined students' perceptions about the use of video games in the classroom. 200 students were surveyed (103 females, 97 males) from flemish secondary schools. (c) The students were also asked about how frequently they played video games. 21.4% of female students and 11.3% of male students replied that they did not play video games. Construct a 95% confidence interval for the difference in the proportion of male and female students that do not play video games. [1] (d) The students preferred medium for playing video games is recorded in the table below. Is there any evidence of an association between gender and preferred medium for playing video games? State the null and alternative hypotheses, and use an appropriate test statistic to determine the P-value. What do you conclude? 3] Console Portable Other Computer device Female 13 6 36 26 Male 26 7 43 10

Answer 1

Bolution Given that: 200 students were surveyed (103 females, 9a mates) (0) Given Male = 11:37 &n=97 -103 20.113 Female = 91.41 = 0.214 $951. confidence interval for the difference Po the proportion of male & female student that do not play video games- = {e=) f (tele de Fat 0 2 4 60400) = (4 13-ozva)t (1932 (10138 0989)(0916 2018 = [(-0.101+ (1.992 * 0.100 + 0.168 4 103

= [(-0-101+ (1.9994J0-90103+0.001635) = {2-01017 (1199* Jo.00663)) = {6-0-1017 (1.920 * 0.0546 = [(-0.101 + (0-10182)] -0.101 0.101820] -14-0101 -0.1018 ) , (-0·lot +0.1018)] -0.0078, 00008] tiere interval include null value tence it is not significant (1) -> Here we have given observational table-

Console. Portable device computer other و Female 13 Hale / 26 T 39 به | 43 79 | 10 36 86 167] تی To Test :- +10: There is no association between gendet e preferred medium for playing video games. Vs *tha There is association between gender. I preferred medium for playing video games. Test statistics :- Y? Ee loij- Eij 12 EN where ons = observed frequency , tij < Expected toeg. Nowo, we need to calculate. Expectation table.

Fi (EN) *(Eti) tee N=167 computer other | Console Portable device 18.9161 0-5638 6.3053 Female 38.3173 17.4610 Male 20.0838 6.6946 406826 18.5389 fu (81*39) - 167 = 3159 167 218.9161 F12 = (81*13) : 162 - 1053 = 167 6.3053 £13 (81*797 167

6399 j63 13 = 38 3193 F11 : (2 x36) 63 - บ6 161 3916 Fy - 11:4610 Es) - (86 * 39) [G - 3359 16 F21 - 20 : 0838 F53 : (86 * !3) 163 (118 29} * 22 - 6 : 6946

(bt * 98) = EY ____ t9 16 13 - 40.68 26 E२८ - (86* 36) 167 3,096 161 - 18.5389 F24 1- (13-18:१161), (6 - 6 -3053) . (36-38-3173) ४.१।61 6.3053 3.3/23 + (२6 - 17-4610) । (२6 - २०- 0833), (१- 6-6५५८) 12-4610 20.0838 6.6946 + (43 - 40-6826) (Ho - (8• 53६५) ५. 6826 1 85389 (- 5.१161), (-0.2013), (-२. 3173) + (8.161 6 3053 28.3123

(4-539) 5916227 (0.23050 15.gle 20.0838 19.4610 6'6946 60-6826 +1-8.5389) 7 18.5389 - 135.0002 +0.0932 +: 5:3698 772.914 118.91616:3053 38:3193 19:4610 + 39.0014 + 0.0932 + 5.3903 +72-91287 20.0838 6.6946 40.6826 185389 J 01-8502 + 0.0147 +0.14014 + 41758 + 1.742.7 +0:1393 +0.1320+ 3.93293 ME 12:12774 df = (2-1)*(4-1) - 183 :: 82 critical value = for 250-05 / Assume) 67.815

p value = <0.00001 Decision: We reject to , if p value ex Value using p value approach. Here p value <a value Hence we reject to Conclusion - There is association between gender & preferred medium for playing video game;