Question

# Prenatal vitamins and Autism. Researchers studying the link between prenatal vitamin use and autism surveyed the...

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

(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.

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