Researchers at the University of Coffeeville in NYC performed a cohort study to investigate the relationship between maternal smoking in pregnancy and adolescent obesity. To ensure that the study population was representative of the Coffeeville population, they randomly selected 600 infants at birth across Coffeeville. Subjects were followed to age 17 to determine if smoking status of the mother during pregnancy is associated with obesity status at age 17. Several subjects were lost to follow-up resulting in only 450 teens contributing obesity data at the close of the study. The classifications are presented in the 2x2 table below.

Maternal Smoking Status During Pregnancy Obesity Status at age 17 Obese Non-Obese Total Smoked throughout 23 75 98 Never Smoked 49 303 352 Total 72 378 450 According to data from the CDC's Youth Risk Behavior Surveillance System (YRBSS), the prevalence of obesity among 17 years olds in Coffeeville is 11%. Using the z-test for a single proportion, test whether the proportion of obese children in this study differs from that of the Coffeeville population of 17 year old teens. Test at the 5% level of significance. [Use the 7-step hypothesis testing procedure].

a) Using correct statistical notation, state the appropriate null and alternative hypotheses.

b) State the rejection region at the 5% alpha level i.e. determine the decision rule.

c) Compute the value of your test statistic.

d) Sketch the appropriate curve to aid in your decision to reject or fail to reject the null hypothesis.

e) Do you reject or fail to reject the null hypothesis? Why or why not? f) State your practical conclusion.

g) Report the p-value

h) Construct a 95% CI for the sample proportion. Interpret this interval for your research colleagues. i) Your principal investigator asks you to write a draft of the conclusion of your study. What will you write (if anything) about the difference in the prevalence of obesity in your sample population vs. the Coffeeville population of 17 year old teens?