Question

Weightlifters at a gym are studying the relationship between supplement type and type of training. They hypothesize the distribution of supplements of people training should be similar to the population. The distribution of the population the gym serves: 43% whey, 46% isolate, 7% casein, 4% undecided. They have supplement data on 200 lifters who train at the gym. Verify if their hypothesis is correct assuming level of significance to be 5%.

Supplement	# of Lifters
Whey	85
Isolate	65
Casein	45
Undecided	5

Answer 1

null hypothesis:Ho:distribution sample is same as distribution in population.

Alternate hypothesis:Ha:distribution sample is not same as distribution in population.

degree of freedom =categories-1=			4
for 0.05 level and 4 df :crtiical value X2 =			9.488	from excel: chiinv(0.05,4)
Decision rule: reject Ho if value of test statistic X2>9.488

applying chi square goodness of fit test:

	relative	observed	Expected		Chi square
Category	frequency(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
1	0.43	85	86.00		0.01
2	0.46	65	92.00		7.92
3	0.07	45	14.00		68.64
4	0.04	5	8.00		1.13
total	1.00	200	200		77.70
test statistic X2=		77.703

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that distribution is different as stated above,