Question

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. ​ Refer to Exhibit 11-2. The calculated value for the test statistic equals

Answer 1

Solution:

Given:

	Expected %	Oi: Observed frequency
Freshman	30%	83
Sophomore	24%	68
Junior	26%	85
Senior	20%	64
		300

We have to find the calculated value for the test statistic.

Chi square test statistic for goodness of fit

Where

O_i = Observed Counts

E_i =Expected Counts = N * % = 300 * % values.

Thus we need to make following table

	Expected %	Oi: Observed frequency	Ei: Expected frequencies	Oi^2/Ei
Freshman	30%	83	90	76.544
Sophomore	24%	68	72	64.222
Junior	26%	85	78	92.628
Senior	20%	64	60	68.267
		N = 300

Thus