4. [6] A team of eye surgeons has developed a new technique for a risky eye oper

Question

4. [6] A team of eye surgeons has developed a new technique for a risky eye operation to restore the sight of people blinded from a certain disease. Under the old method, it is known that only 30% of the patients who undergo this operation recover their eyesight. Suppose that surgeons in various hospitals have performed a total of 225 operations using the new method and that 88 have been successful (i.e., the patients fully recovered their sight). Is there statistically significant evidence to justify the claim that the new method has a success rate that is higher than 30% and better than the old method? Use = 0.05 as the level of significance. make sure you state 1. the hypotheses, 2. the value of the test statistic z, 3. the p-value, 4. your statistical conclusion, and 5. your practical conclusion.

Explanation / Answer

A. The level of significance is = 0.05. Let p be the probability that patient recoves fully.the null hypothesis is that p is still 0.30 even for new method. the new method has improved chances of a patient recovering his eyesight. Hence,

Ho: p=0.30,H1:p>0.30

B. using p from Ho, we note that np=225(0.30)=67.5

is greater than 5 and that nq=225(0.70)=157.5 is also greater than 5. we use normal distribuiton for sample statistic p'

we are given

p'=88/225=0.3911
test statistic z=(.3911-.30)/sqrt[p(1-p)/n)] = (.3911-.30)/sqrt[(.30 (.70)/225)] = 2.98

from normal table, p-value is .0014 (for 1-sided test), and .0028 for 2 sided test

the value for p is from null hypothesis.Ho specifies that p=0.30 so q=1-p=0.70

C. since we have right tailed test, the p-value is area of the right (z=2.98).using the normal distribution calculator, we find p-value=P(z>2.98)=0.0016

D. finally to conclude ,since the sample statistic doesnot fall in critical region, we fail to reject Ho, and conclude that 5% level of significance the evidence is not strong enough to reject the claim.this result is consistent with conclusion obtained by using p-value method.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

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