Question

The table lists the number of students from three different high schools participating in the mathematics and physics sections of a science fair High School 1 High School 2 High School 3 Mathematics 7 7 18 Physics 37 17 21

Given the following results.

a) State the alternative hypothesis statement. (1 mark)

b) State the degrees of freedom. (1 mark)

c) Find the value of A, B, and C. d) Using the p-value method, at α = 0.05, test the claim that the section of participation and the high school where the students were from are independent.

Answer 1

(a) The section of participation and the high school where the students were from are dependent

(b) 2

(c)

		High School 1	High School 2	High School 3	Total
Mathematics	Observed	7	7	18	32
	Expected	13.16	7.18	11.66	32.00
	O - E	-6.16	-0.18	6.34	0.00
	(O - E)² / E	2.88	0.00	3.44	6.33
Physics	Observed	37	17	21	75
	Expected	30.84	16.82	27.34	75.00
	O - E	6.16	0.18	-6.34	0.00
	(O - E)² / E	1.23	0.00	1.47	2.70
Total	Observed	44	24	39	107
	Expected	44.00	24.00	39.00	107.00
	O - E	0.00	0.00	0.00	0.00
	(O - E)² / E	4.11	0.01	4.91	9.03
		9.03	chi-square
		2	df
		.0109	p-value

(d) The p-value is 0.0109.

Since the p-value (0.0109) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the section of participation and the high school where the students were from are dependent.