Question

A random group of oranges were selected from an orchard to analyze their ripeness. Based on the time of year, the orchard owner believes that 15% of the oranges are ready for picking now, 35% will be ready in three days, 30% will be ready in one week, and 20% will be ready in two weeks. Is there evidence to reject this hypothesis at = 0.05? Ready to pick Ripe Ready in three days Ready in one week Ready in two weeks Number of oranges 12 15 15 16 A) There is not evidence to reject the claim that the oranges are distributed as claimed because the test value 4.635 < 7.815 B) There is evidence to reject the claim that the oranges are distributed as claimed because the test value 9.488 > 4.635 C) There is evidence to reject the claim that the oranges are distributed as claimed because the test value 5.991 > 4.635 D) There is not evidence to reject the claim that the oranges are distributed as claimed because the test value 4.635 < 9.488

Answer 1

at 0.05 level and (categories-1=3) degree of freedom critical value of chi square =7.815

applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
now	0.150	12.000	8.700		1.252
3 days	0.350	15.000	20.300		1.384
1 week	0.300	15.000	17.400		0.331
2week	0.200	16.000	11.600		1.669
total	1.000	58	58		4.635

option A is correct

A) There is not evidence to reject the claim that the oranges are distributed as claimed because the test value 4.635 < 7.815