Question

1. The following table compares musical genre preference with preferred leisure activity among Mary's goats.

Music:	Jazz	Opera	M.R.F.
Kicking Humans	27	32
Reading	35	31
Eating Flowers	41	26
Arson	7	18
Marginal Relative Frequency

1. Complete a marginal relative frequency distribution above.
2. What proportion of Mary's goats enjoy peaceful activities (reading, eating flowers)?
3. Does it seem that musical preference and preferred leisure activity are independent? Justify your answer.

Answer 1

(a) the marginal relative frequency are given as

Music	Jazz	Opera	MRF
Kicking Humans	27/219=0.1244	0.1475	59/217=0.2719
Reading	0.1613	0.1429	0.3041
Eating Flowers	0.1889	0.1198	0.3088
Arson	0.0323	18/219=0.0829	0.1152
Marginal Relative Frequency	110/217=0.5069107/219=	0.4931	1

(b) required proportion =0.3041+0.3088=0.6129

(c) here we use chi-square test with  

null hypothesis H0: musical preference and preferred leisure activity are independent

and alternate hypothesis Ha:musical preference and preferred leisure activity are not independent

test statistic chi-square=sum((O-E)2/E)=8.82 with (r-1)(c-1)=(4-1)(2-1)=3 df

and typical critical chi-square=(0.05,3)=7.81 is less than calculated chi-square=8.82, so we reject the null hypothesis and conclude that :musical preference and preferred leisure activity are not independent

	Observed(O)	Expected(E)	E	(O-E)	(O-E)2/E
	27	110*59/217	29.91	-2.91	0.28
	35	110*66/217	33.46	1.54	0.07
	41	110*67/217	33.96	7.04	1.46
	7	110*25/217	12.67	-5.67	2.54
	32	107*59/217	29.09	2.91	0.29
	31	107*66/217	32.54	-1.54	0.07
	26	107*67/217	33.04	-7.04	1.50
	18	107*25/217	12.33	5.67	2.61
	217	0	217	0	8.82
			critical	chi-square(0.05,3)=	7.81