Question

2. At an alpha of 0.05, does someone’s age depend on whether or not they believe that vaccination for MMR (Measles, Mumps, Rubella) should be mandated for students entering pre-school and grade school.   The numbers represent the count of “yes” and “no” responses for each age level.

	<20	20, <25	25, <30	30, <35	35, <40	>=40
Yes	10	7	14	20	16	18
No	12	5	6	4	2	1

Answer 1

Null hypothesis Ho : Age and whether or not they believe that vaccination for MMR are independent

Alternate hypothesis : H1: Age and whether or not they believe that vaccination for MMR are dependent

Chi-square test for independence is appropriate for this.

Test Statistic

O : Observed Frequency

E: Expected Frequency

Observed Counts/Frequency	<20	20, <25	25, <30	30, <35	35, <40	>=40	Row Total
Yes	10	7	14	20	16	18	85
No	12	5	6	4	2	1	30
Column Total	22	12	20	24	18	19	115

E: Expected Frequency	<20	20, <25	25, <30	30, <35	35, <40	>=40
Yes	(85*22) / 115	(85*12) / 115	(85*20) / 115	(85*24) / 115	(85*18) / 115	(85*19) / 115
No	(30*22) / 115	(30*12) / 115	(30*20) / 115	(30*24) / 115	(30*18) / 115	(30*19) / 115

E:	<20	20, <25	25, <30	30, <35	35, <40	>=40
Yes	16.2609	8.8696	14.7826	17.7391	13.3043	14.0435
No	5.7391	3.1304	5.2174	6.2609	4.6957	4.9565

O	E	O-E	(O-E)2	(O-E)2/E
10	16.2609	-6.2609	39.1985	2.4106
7	8.8696	-1.8696	3.4953	0.3941
14	14.7826	-0.7826	0.6125	0.0414
20	17.7391	2.2609	5.1115	0.2882
16	13.3043	2.6957	7.2665	0.5462
18	14.0435	3.9565	15.6541	1.1147
12	5.7391	6.2609	39.1985	6.8300
5	3.1304	1.8696	3.4953	1.1165
6	5.2174	0.7826	0.6125	0.1174
4	6.2609	-2.2609	5.1115	0.8164
2	4.6957	-2.6957	7.2665	1.5475
1	4.9565	-3.9565	15.6541	3.1583
			Total	18.3813

Test Statistic:

Degrees of freedom= (Number of rows -1) x (Number of columns -1)=(2-1)x(6-1)=5

for 5 degrees of freedom,

Alpha : = 0.05

As p-value : 0.0025 < Alpha : : 0.05 ; reject the null hypothesis.

At an alpha of 0.05 there is sufficient evidence to conclude that : someone’s age depend on whether or not they believe that vaccination for MMR (Measles, Mumps, Rubella) should be mandated for students entering pre-school and grade school