A random group of oranges were selected from an orchard to analyze their ripenes

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

Explanation / Answer

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:

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

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

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