Question

In this month’s GOOP magazine, healing oils were recommended as a preventative measure for measles. In South Texas, families with children <5 years old were sampled about questions regarding their child’s vaccination status. The research showed that there was a large proportion of the population that used healing oils instead of traditional vaccination.  Further testing for measles yielded the following observed frequencies:

		Measles
		Yes	No
Treatment	Vaccine	6	3494
	Oils	3000	3500

Using a 0.01 significance level, you need to test the claim that the treatment (vaccine or oils) is independent of whether a child contracted measles. If you are a parent who is using healing oils as a method to prevent against measles, should you be concerned about your child contracting measles?

1. Fail to reject the null and conclude there is sufficient evidence to support the claim that vaccination is independent of contracting the measles.
2. Fail to reject the null and conclude there is not sufficient evidence to support the claim that vaccination or oils is independent of contracting the measles.
3. Reject the null hypothesis and conclude there is sufficient evidence to warrant rejection of the claim that the treatment and reaction are independent.
4. Reject the null hypothesis and conclude there is not sufficient evidence to warrant rejection of the claim that the treatment and reaction are dependent.
5. Since 2,287.87 lies within the confidence interval 2000-3000, we are rejecting the null hypothesis and concluding that the treatment and reaction are dependent.

Answer 1

Observed
	Yes	No	total
Vaccine	6	3494	3500
Oil	3000	3500	6500
Total	3006	6994	10000

Expected frequency, Ei = sum(rowi)*sum(coli)/total

Expected
	Yes	No
Vaccine	1052.100	2447.900
Oil	1953.900	4546.100

test statistic, chi-square = sum((Oi - Ei)^2/Ei) = 2287.97

p-value = 0

Reject H0

Reject the null hypothesis and conclude there is sufficient evidence to warrant rejection of the claim that the treatment and reaction are independent.