Question

The principal of Paul Revere High School bragged that his 2016 graduating class of 1500 students achieved impressive scores on their ACT exams. He announced that an “astounding” 36% of the class got a score of 29 or higher, 54% got a score of 21 to 28, and only 10% less than 21. You want to test whether these ACT results are really that astounding. You visit the ACT website to see that the national results are 34% getting a score over 28, 58% getting 21 to 28, and 8% less than 21. Test whether or not the principal is correct to brag that his proportions were more impressive than the national performance. Use an alpha of .05.

To the nearest hundredth, what is the calculated value for chi-square in this example?

Answer 1

for 0.05 level and 2 degree of freedom :rejection region =

5.991

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
>=29	0.340	540.000	510.00	1.33	1.765
21-28	0.580	810.000	870.00	-2.03	4.138
<=21	0.080	150.000	120.00	2.74	7.500
total	1.000	1500	1500		13.4026
test statistic X2 =		13.40

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that proportions were different than the national performance.