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6.34 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 (periconceptional period). (Schmidt, 2011)

	Autism	Typical Development	Total
No vitamin	111	70	181
Vitamin	143	159	302
Total	254	229	483

(a) State appropriate hypotheses to test for independence of use of prenatal vitamins during the three months before pregnancy and autism.

Ho: p_vitamin = p_{no vitamin}
Ha: p_vitamin < p_{no vitamin}
Ho: p_vitamin = p_{no vitamin}
Ha: p_vitamin ≠ p_{no vitamin}
Ho: p_vitamin = p_{no vitamin}
Ha: p_vitamin > p_{no vitamin}

(b) Complete the hypothesis test and state an appropriate conclusion.
What is the value of the test statistic for this test? (Please round to two decimal places) What is the p-value associated with this test? (Please round to four decimal places) The result of the hypothesis is:

Since p<α we reject the null hypothesis and accept the alternative
Since p ≥ α we do not have enough evidence to reject the null hypothesis
Since p ≥ α we accept the null hypothesis
Since p ≥ α we reject the null hypothesis and accept the alternative
Since p<α we fail to reject the null hypothesis

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