In 2012 the Centers for Disease Control and Prevention reportedthat in a sample of 4,349 African Americans 31% were Vitamin Ddeficient. A 90% confidence interval based on this sample is (0.30,0.32). It is believed that among the general population ofAmericans 8% suffer from Vitamin D deficiency.
Define the appropriate parameter and state the appropriatehypotheses for testing the claim that, among African Americans,Vitamin D deficiency occurs at a rate other than 8%.
Does this confidence interval provide evidence that amongAfrican Americans Vitamin D deficiency occurs at a rate other than8%? What significance level is being used to make this decision?Briefly justify your answer.
Using the definition of a p-value, explain why the area in thetail of a randomization distribution is used to compute ap-value.
In a test of the hypotheses vs. , the observed sample results ina p-value of 0.0256. Would you expect a 95% confidence interval forbased on this sample to contain 0? Briefly explain why or whynot.
