Question

A report on health care in the United States said that 28% of Americans have experienced times when they haven't been able to afford medical care. A news organization randomly sampled 801 black Americans, of whom 38% reported that there had been times in the last year when they had not been able to afford medical care. Does this indicate that this problerm is more severe among black Americans? Test an appropriate hypothesis (show your work, and state your condusion.

Answer 1

see here we are given ,

p=proportion of Americans had not been able to affort medical care = 0.28

now we take sample of 801 black Americans

so n=sample size = 801 , and p^ =sample proportion of Americans had not been able to affort medical care = 0.38

Here we have to test this problem is more severe amoung Black Americans .

H0 : p = 0.28 vs H1: p > 0.28

We used here one sample proportion test

formula of test statistics is

$Z=\frac{\hat{p}- p}{\sqrt {\frac{{p * (1-p)}}{}{n}}}$

$Z=\frac{0.38- 0.28}{\sqrt {\frac{{0,28 * (1-0.28)}}{}{801}}}$

Z = 6.25

Now we have to find pvalue

pvalue = P( Z > 6.25) = 0

here pvalue= 0 is less than alpha=0.05 thne we reject H0

conclusion : so we support H1 means proportion is greater than p

more sever black Americans