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). (Use a significance level of 0.05. Use

p_V p_NV.)

		Autism
		Autism	Typical development	Total
Periconceptional prenatal vitamin	No vitamin	113	70	183
Vitamin	144	157	301
	Total	257	227	484

(a)State appropriate hypotheses to test for a difference in the rates of autism of children of mothers who did use prenatal vitamins during the first three months before pregnancy and the rates of autism of children of mothers who did not use prenatal vitamins during the first three months before pregnancy.

H₀: p_V > p_NVH_A: p_V p_NV

H₀: p_V p_NVH_A: p_V = p_NV

H₀: p_V p_NVH_A: p_V p_NV

H₀: p_V = p_NV H_A: p_V p_NV

H₀: p_V p_NV H_A: p_V > p_NV

(b)Complete the hypothesis test and state an appropriate conclusion.Check the relevant conditions.

The sample ---Select--- is is not random and the sample represents ---Select--- greater than less than 10% of all mothers of autistic children and mothers of children with a typical development. Therefore whether or not one mother in the sample took prenatal vitamins in the three months before pregnancy ---Select--- is is not independent of another. The success-failure condition ---Select--- is is not met since the number of successes and failures is ---Select--- greater than less than 10.

Calculate the test statistic and determine the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.)z=p-value=Interpret the p-value in context of the hypothesis test and the data.

Fail to reject H₀. The data do not provide strong evidence of a difference in the rates of autism of children of mothers who did and did not use prenatal vitamins during the three months before pregnancy.

Fail to reject H₀. The data provide strong evidence of a difference in the rates of autism of children of mothers who did and did not use prenatal vitamins during the three months before pregnancy.

Reject H₀. The data do not provide strong evidence of a difference in the rates of autism of children of mothers who did and did not use prenatal vitamins during the three months before pregnancy.

Reject H₀. The data provide strong evidence of a difference in the rates of autism of children of mothers who did and did not use prenatal vitamins during the three months before pregnancy.

(c)A New York Times article reporting on this study was titled "Prenatal Vitamins May Ward Off Autism." Do you find the title of this article to be appropriate? Explain your answer. Additionally, propose an alternative title.

Yes, this title is appropriate, because the data support the claim that prenatal vitamins may ward off autism.

No, the title is not appropriate, because the study was observational and we cannot make causal claims based on observational studies. "Mothers who use prenatal vitamins before pregnancy are found to have children with a lower rate of autism" would be more appropriate.

No, this title is not appropriate, because the data do not support the claim that prenatal vitamins may ward off autism. "Prenatal Vitamins Do Not Ward Off Autism" would be a more appropriate title.