Question

A sharp-minded lad (who tended to be compulsive) recorded each card played at a bridge tournament as a "point card" (Jack through Ace) or "no-point card" (10 through 2). His theory was that there were some shenanigans going on instead of fair playing of the card. Test the data with a chi square and write a conclusion. A bit of thinking required in this one to set up. First, show all your work on how you obtained all of the expected f and totals, then write out your formula(s) and show all your work in plugging in the numbers, including df and critical values.

point cards	no-point cards
130	270

Answer 1

null hypothesis: game is fair or p_{point cards} =4/13 ; p_{no-point cards} =9/13

alternate hypothesis:game is not fair or p_{point cards} 4/13 ; p_{no-point cards}9/13

degree of freedom =categories-1=2-1=1

for 1 df and 0.05 level rejection region >3.841

applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
point cards	4/13	130.000	123.077		0.389
No 'point cards	9/13	270.000	276.923		0.173
total	1.000	400	400		0.562

as test statistic 0.562 is not in rejection region we can nt reject null hypothesis

we do not have evidence to cnclude that game is not fair.