1.In July 2008 the US National Institutes of Health announced that it was stopping a clinical study early because of unexpected results. The study population consisted of HIV-infected women in sub-Saharan Africa who had been given single dose Nevaripine (a treatment for HIV) while giving birth, to prevent transmission of HIV to the infant. The study was a randomized comparison of continued treatment of a woman (after successful childbirth) with Nevaripine vs. Lopinavir, a second drug used to treat HIV. 240 women participated in the study; 120 were randomized to each of the two treatments. Twenty-four weeks after starting the study treatment, each woman was tested to determine if the HIV infection was becoming worse (an outcome called virologic failure). Twenty-six of the 120 women treated with Nevaripine experienced virologic failure, while 10 of the 120 women treated with the other drug experienced virologic failure.A two-way table presenting the results of this study is given below.

Virologic Failure

Yes

No

Total

Treatment

Nevaripine

26

94

120

Lopinavir

10

110

120

Total

36

204

240

(1)State appropriate hypotheses to test for association of treatment and virologic failure.

(2)Complete the hypothesis test and state an appropriate conclusion. (Reminder: Verify any necessary conditions for the test.)

2.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).

Autism

Autism

Typical development

Total

Periconceptional prenatal vitamin

No vitamin

111

70

181

Vitamin

143

159

302

Total

254

229

483

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

(2)Complete the hypothesis test and state an appropriate conclusion. (Reminder: Verify any necessary conditions for the test.)

(3)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.