Question

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 (periconceptional period).

1) Complete the hypothesis test and state an appropriate conclusion.

Autism Typical Development TOTAL Periconceptual No vitamin 111 70 181 Prenatal vitamin Vitamin 143 159 302 TOTAL 254 229 483

Answer 1

The appropriate Null and Alternative Hypotheses are given below: From the given information, the claim of the problem is testing whether the variables prenatal vitamin use and autism are dependent or not. Null hypothesis: Ho: The variables prenatal vitamin use and autism are independent. Alternative hypothesis: H: The variables prenatal vitamin use and autism are not independent. The test statistic value is 3.8647 and it is obtained below: From the given information, Autism Total Typical Development 70 No 111 181 vitamin Vitamin Total 302 143 254 159 229 483

10.-F (0;-E;)E row total x column total Expected value E) = Actual value (0)| N 181x 254 =95.18427 483 250.1373 2.627927 181x 229-85.81573 250.1373 2.914819 483 302 x 254 -=158.8157 483 250.1364 1.57501 302 x 229 >=143.1843 483 250.1364 1.746954 (0;-E:) -8 8647 E The statistic is, Test statistic=2(0;-) E = 8.8647

Decision Rule: If p-value <a, then reject the null hypothesis. If p-value > a, then do not reject the null hypothesis. The p-value is 0.0029 and it is calculated below: The test statistic value is 8.8647. The degrees of freedom is (number of rows-1) (number of columns-1)=(2-1)(2-1)=1. p-value=0.0029 by Excel function "CHISQ.DIST.RT(8.8647,1)" Conclusion: Consider the level of significance is a=0.05 The p-value is 0.0029. Here, the p-value is lesser than the level of significance. That is, p=0.0029) <a=0.05. From the rejection rule, reject the null hypothesis. It can be concluded that "The variables prenatal vitamin use and autism are not independent".