According to a June 2004 Gallup poll, 28% of Americans “said there have been tim

Question

According to a June 2004 Gallup poll, 28% of Americans “said there have been times in the last year when they haven’t been able to afford medical care.” Is this proportion higher for black Americans than for all Americans? In a random sample of 801 black Americans, 34% reported that there had been times in the last year when they had not been able to afford medical care.

a) 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. Use correct notation!

b) Explain Type 1 error in this context

c) Explain Type 2 error in this context

Which error seems to be more serious? Why?

Explanation / Answer

(a) Below are the null and alternate hypothesis are
H0: p <= 0.28
H1: p > 0.28

Test statistics,
t = (pbar - p)/SE = (0.34 - 0.28)/sqrt(0.34*0.66/801) = 3.5847

degrees of freedom = 801 - 1 = 800

p-value = 0.0001789

As p-value is less than the significance level of 0.05, we reject null hypothesis. This means there is significanct evidence that the proportion of black americans who havn't able to afford medical care is greater than the white americans.

(b)
Type I error is the probability when we fail to reject the null hypothesis though actually it should be rejected.

(c)
Type II error is the probability when null hypothesis is rejected though actually it is true. In this example though the proportion of black americans is not greater than the white americans but as the result of hypothesis we rejected the null hypothesis and resulted into acceptance of alternate.

(d)
Type II error is more serious because it results into the acceptance of alternate hypothesis which is the research hypothesis.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.