Question

In 2012, the Centre for Disease Control and Prevention reported that in a sample of African Americans a certain proportion were Vitamin D deficient.

A 95% confidence interval based on this sample is (0.28, 0.34).

It is believed that among the general population of Americans, only 9% suffer from Vitamin D deficiency.

(a) Define the appropriate parameter(s) and state the appropriate hypotheses for testing the claim that, among African Americans the proportion who suffer from Vitamin D deficiency is different from 9%. What is the direction of the test?

(b) Does this confidence interval provide evidence for the alternative which states that among African Americans the proportion who suffer from Vitamin D deficiency is different from 9%?

(YES/NO)

(c) Briefly justify your answer.

(d) What significance level is being used to make this decision?

Answer 1

Ans:

a)

Let p be thet true proportion of Americans who suffer from Vitamin D deficiency.

It is non-directional(two tailed) test.

b)Yes

c)As,the above confidence interval does not include 0.09 within its limits.

d)Significance level=0.05