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	111	65	176
Vitamin	141	159	300
Total	252	224	476

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

H0H0: The variables use of prenatal vitamins during the three months before pregnancy and autism are independent.

HAHA: 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. X2X2 =

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. very strong evidence
B. little evidence
C. strong evidence
D. extremely 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:

Hence,

1. Expected value table is:

Prenatal Vitamin	Autism	Typical Development
No vitamin	93.1765	82.8235
Vitamin	158.8235	141.1765

2.Test statistic: X2 = 11.4954

3. Degrees of freedom = 1

4. p - Value = 0.0007

5. Very strong evidence