A report on health care in the US said that 28 of Americans

A report on health care in the US said that 28% of Americans have experianced times when they have not been able to afford medical care. A new organization randomely sampled 801 African Americans, of whom 38% reported that there had been times when they had not been able to afford medical care. Does this indicate that this problem is more severe among African Americans.

a. State the null hypothesis and what the population parameter represents.

b.Check the conditions for performing a one-proportion z-test.

c. Determine the parameters of the null model

d. Find the p-value

e. State the conclusion for the null hypothesis test.

Solution

Set Up Hypothesis
Null, H0:P=0.28
Alternate, it is more severe among African Americans H1: P>0.28
Test Statistic
Number of objects in a sample provided(n)=801
No. Of Success Rate ( P )= x/n = 0.38
Success Probability ( Po )=0.28
Failure Probability ( Qo) = 0.72
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.38-0.28/(Sqrt(0.2016)/801)
Zo =6.3033
| Zo | =6.3033
Critical Value
The Value of |Z | at LOS 0.025% is 1.96
We got |Zo| =6.303 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail - Ha : ( P > 6.30334 ) = 0
Hence Value of P0.025 > 0,Here we Reject Ho

We have enough evidence to indicate that this problem is more severe among African Americans