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 109 63 172 Vitamin 138 156 294 Total 247 219 466

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 = 0.1?

A. Reject H0H0
B. Do not reject H0H0

1) Each expected value = Row Total * Column Total/total. Here Total = 466

 Expected Autism Typical Total No Vitamin 91.17 80.83 172 Vitamin 155.83 138.17 294 Total 247 219 466

2) The calculation of the test statistic is as below:

 Number Observed Expected (O-E) (O-E)2 (O-E)2/E 1 109 91.17 17.83 318 3.48811449 2 138 155.83 -17.83 318 2.04066562 3 63 80.83 -17.83 318 3.93408346 4 156 138.17 17.83 318 2.30157264 Total 11.7644362

= 11.76

3) The degrees of freedom = (R - 1) * (c - 1) = (2-1) * (2 - 1) = 1 - 1 = 1

4) The p value for = 11.76, df = 1 is p value = 0.0006

5) Since p value (0.0006) is < (0.10), Option A: Reject H0

The Conclusion: There is sufficient evidence at the 10% level of significance to conclude that the variables use of prenatal vitamins during the three months before pregnancy and autism are not independent.

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