(8 points) 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 110 64 174

\ﬁtamin 139 156 295

Total 249 220 469 Conduct the hypothesis test for the stated null and alternative. Use a = K and round numeric answers to four decimal places.

H 0: The variables use of prenatal vitamins during the three months before pregnancy and autism are independent.

H A: 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. X 2 =

3. Calculate the degrees of freedom for this hypothesis test. 4. Calculate the p—value for this hypothesis test. p—value = 5. Based on the p—value, we have: A A. little evidence A B. strong evidence quot; G. some evidence quot; D. very strong evidence E. extremely strong evidence that the null model is not a good fit for our observed data. Statistics and Probability