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 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. What is your conclusion using αα = 0.01?

A. Reject H0H0
B. Do not reject H0H0

Answer 1

(1)

Prenatal vitamin	Autism	Typical Development
No vitamin	262X183/494=97.06	232X183/494=85.94
Vitamin	262X311/494=164.94	232X311/494=146.06

(2)

Test Statistic is calculated as follows:

Observed Frequency (O)	Expected Frequency (E)	(O - E)2/E
116	97.06	3.70
67	85.94	4.18
146	164.94	2.18
165	146.05	2.46
Total = =		12.51

So,

Test statistic = 12.51

(3)

Degrees of Freedom = (r - 1) X (c - 1)

                             = (2 - 1) X (2 - 1)

= 1

So,

Degrees of Freedom = 1

(4)

By Technology, p - value= 0.0004

(5)

Since p - value = 0.0004 is less than = 0.01, the difference is significant. Reject null hypothesis.

So,

Correct option:

A.   Reject H0.