Practice Task:

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 problem is more severe among black Americans?

Test an appropriate hypothesis and state your conclusion. (Make sure to check any necessary conditions and to state a conclusion in the context of the problem.)
Include:
•	Condition Check
•	The Claim
•	Ho and Ho both in English and using Symbols
•	The test statistic and a p-value
•	A decision
•	A statement about your decision in terms of the claim

Create a 95% confidence interval and make a confidence statement to interpret the result about estimating the proportion of black Americans who have had to forgo health care due to cost. Also compare this result to your significance test. Does it confirm your earlier decision? Explain.

Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than 85% of firms in the manufacturing sector still do not offer any child-care benefits. A random sample of 330 manufacturing firms is selected, and only 26 of them offer child-care benefits. 

Test an appropriate hypothesis and state your conclusion. (Make sure to check any necessary conditions and to state a conclusion in the context of the problem.)
Include:
•	Condition Check
•	The Claim
•	Ho and Ho both in English and using Symbols
•	The test statistic and a p-value
•	A decision
•	A statement about your decision in terms of the claim

Create a 95% confidence interval and make a confidence statement to interpret the result about estimating the proportion of manufacturing sector companies who still do not offer any child-care benefits. Also compare this result to your significance test. Does it confirm your earlier decision? Explain.

1) Hypotheses: : p = 0.28. The proportion of all black Americans that were unable to afford medical care in the last year is 28%.
: p > 0.28. The proportion of all black Americans that were unable to afford medical care in the last year is greater than 28%.

Model: Okay to use the Normal model because the sample is random, these 801 black Americans are less than 10% of all black Americans, and np = (801)(0.28) = 224.28 > 10 and nq = (801)(0.72) = 576.72 > 10. 
We will do a one-proportion z-test.
Mechanics: n = 801,  = 0.38
z = 
P = P( > 0.38) = P(z > 6.29) ≈ 0
Conclusion: With a P-value so small (barely above zero), I reject the null hypothesis. There is evidence to suggest that the proportion of black Americans who were not able to afford medical care in the past year is more than 28%.
2) One-tail, upper tail test. We are concerned that the proportion of people who are not able to afford medical care is higher among black Americans.
3) If the proportion of black Americans was 28%, we would almost never expect to find at least 38% of 801 randomly selected black Americans responding “yes.”