Question

Prenatal vitamins and Autism. Researchers studying the link between prenatal vitamin use and autism surveyed the mothers of a random sample of children aged 24 - 60 months with autism and conducted another separate random sample for children with typical development. The table below shows the number of mothers in each group who did and did not use prenatal vitamins during the three months before pregnancy.

Prenatal Vitamin	Autism	Typical Development	Total
No vitamin	116	67	183
Vitamin	146	165	311
Total	262	232	494

Conduct the hypothesis test for the stated null and alternative. Use ?α = K and round numeric answers to four decimal places.

?0H0: The variables use of prenatal vitamins during the three months before pregnancy and autism are independent.

??HA: The variables use of prenatal vitamins during the three months before pregnancy and autism are not independent.

1. Enter the expected values for the hypothesis test in the table below, rounded to four decimal places.

Prenatal Vitamin	Autism	Typical Development
No vitamin
Vitamin

2. Calculate the test statistic for this hypothesis test. ?2X2 =

3. Calculate the degrees of freedom for this hypothesis test.

4. Calculate the p-value for this hypothesis test. p-value =

5. Based on the p-value, we have:
A. little evidence
B. very strong evidence
C. extremely strong evidence
D. some evidence
E. strong evidence
that the null model is not a good fit for our observed data.

Answer 1

a)

Ei=row total*column total/grand total	Autism	Typical
No vitamin	97.0567	85.9433
Vitamin	164.9433	146.0567

b)

Applying chi square test of independence:

chi square    χ2	=(Oi-Ei)2/Ei	Autism	Typical	Total
	No vitamin	3.6973	4.1754	7.8727
	Vitamin	2.1756	2.4569	4.6325
	total	5.8729	6.6323	12.5052
test statistic X2 =		12.5052

c)

degree of freedom(df) =(rows-1)*(columns-1)=

1

d)

p value =

0.0004

e)

option C is correct