Question

The admissions office at Huge U. believes the geographical distribution of entering students may be changing. over the last 30 years, 45% of the students have come from Midwestern states, 20% from the Southwest, 20% from the coasts, 5% from the South, and 10% from the Northwest. A sample of 250 students from this year's entering class includes 96 from the Midwest, 61 from the Southwest, 45 from the coasts, 17 from the South, and 31 from the Northwest. Does this indicate that the current entering class has a different geographical distribution?

Answer 1

here null hypothesis:Ho: current entering class has same geographical distribution

alternate hypothesis:Ha" current entering class has a different geographical distribution

degree of freedom =categories-1=

4

for 0.05 level and 4 degree of freedom :rejection region =

9.488

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Midwestern	0.450	96	112.50	-1.56	2.420
Southwest	0.200	61	50.00	1.56	2.420
Coast	0.200	45	50.00	-0.71	0.500
South	0.050	17	12.50	1.27	1.620
Northwest	0.100	31	25.00	1.20	1.440
total	1.000	250	250		8.400

as test statistic =8.40 is not in critical region ; we can not reject null hypothesis

we do not have evidence at 0.05 level to conclude that current entering class has a different geographical distribution