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	68	184
Vitamin	147	166	313
Total	263	234	497

Conduct the hypothesis test for the stated null and alternative. Use αα = K and round numeric answers to three 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 three 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. What is your conclusion using αα = 0.01?

A. Do not reject H0H0
B. Reject H0H0

Answer 1

1)

Expected	Ei=Σrow*Σcolumn/Σtotal	Autism	Typical development	Total
	No vitamin	97.368	86.632	184
	Vitamin	165.632	147.368	313
	Total	263	234	497

2)

chi square    χ2	=(Oi-Ei)2/Ei	Autism	Typical development	Total
	No vitamin	3.570	4.010	7.580
	Vitamin	2.100	2.360	4.460
	Total	5.670	6.370	12.040

  test statistic for this hypothesis test=12.040

3)

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

1

4)

p-value for this hypothesis test=0.0005

5)B. Reject H0