Question

1. The advisors of Ecology club at a large college believes that the group consists of 10% freshman, 20% sophomores, 40% juniors and 30% seniors. The membership for the club this year consisted of 14 freshmen, 19 sophomores, 51 juniors and 16 seniors. At α=10% test the advisors conjectu

Answer 1

Step 1:

H0​: Proportion of group Pfres = 0.10 , Psop​h = 0.20 , Pjun ​= 0.40 , Psen ​ = 0.30

Ha: Population proportions differ from the values stated in the null hypothesis

We will conduct Chi-Square test for Goodness of Fit to test the hypothesis.

Step 2: Test statistics

Create below table based on observed and expected frequencies.

Group	Observed values (fo)	Expected Proportions	Expected (fe)	(fo-fe)2/fe
Freshman	14	0.10	10	1.600
sophomores	19	0.20	20	0.050
juniors	51	0.40	40	3.025
seniors	16	0.30	30	6.533
Sum	100	1.00	100	11.208

Step 3: Rejection region

Level of significane = 0.10

d f =4−1=3

critical is equal to  6.251

Since ( 11.208) is greater than critical (6.251) , we reject the Null hypothesis.

We have sufficient evidence to belive that the population proportions for all four groups differ from that stated in the Null hypothesis.