HS Sophomore students organized a pep-rally and 50 students from all years (F, S, J, Seniors) were selected to participate (it was an honor). The Sophomores picked the students from each level. An ANOVA analysis was done by the faculty sponsor to assess whether the results were rigged in favor of the Sophomores.

Here are the results of the Sophomore selections: Of the 50 slots filled: 15 were Freshmen, 20 were sophomores, 10 were Juniors, and 5 were Seniors. But, of the entire school population: 30% are Freshmen, 25% are sophomores, 25% are Juniors, and 20% are Seniors. Were the selections biased?

a) State your Ho: ________________ , and Ha: __________________ Assume a significance level of 5%

b) Fill in the following Table and do the necessary calculations.

Class	Observed	Expected	((E - O) 2 / E
Freshmen
Sophomores
Juniors
Seniors
		Total is the X2 Test >>

X²Teststatisticis________

b) Number of outcomes (number of class levels): k = _____; Degrees of Freedom (df) = (k - 1) = ______

c) X²Critical(from the Table) is _______

d)Accept or Reject Ho ? ____________; Real world interpretation?_______________

e)From software what is the p-value and is it less or greater than our of 5% ?