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 256 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 problem is more severe among black Americans? Construct an appropriate Hypothesis Test to answer this question. Use a 95 percent level of confidence. Show work.

Answer 1

Null hypothesis  
H0: p = 0.28                  
                      
Alternative hypothesis
H1: p > 0.28                      
                      
We have for given example,                      
Population proportion value is =0.28                  
x=256                  
                      
n=801                  
Level of significance =   0.05                  
Estimate for sample proportion =
                      
Z test statistic formula for proportion

P value is 0.0063.................by using Excel command 1-NORMSDIST(2.496) or by using Z table.

P value is 0.0063 < 0.05

Therefore, we reject H0 at

Conclusion: We have sufficient evidence at to say that,  this problem is more severe among black Americans.