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	110	65	175
Vitamin	141	158	299
Total	251	223	474

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. strong evidence
C. extremely strong evidence
D. very strong evidence
E. some evidence
that the null model is not a good fit for our observed data.

Answer 1

The statistical software output for this problem is :

Contingency table results:
Rows: Prenatal Vitamin
Columns: None

Cell format
Count (Expected count)

	Autism	Typical Development	Total
No vitamin	110 (92.6688)	65 (82.3312)	175
Vitamin	141 (158.3312)	158 (140.6688)	299
Total	251	223	474

Chi-Square test:

Statistic	DF	Value	P-value
Chi-square	1	10.922088	0.001

Test statistics = 10.9221

Degrees of freedom = 1

P-value = 0.001

D. very strong evidence