Answer to Question #213377 in Statistics and Probability for arwa

Question

 Q waves on the electrocardiogram, according to Schinkel et al. (A-15), are often considered to be

reflective of irreversibly scarred myocardium. These researchers assert, however, that there are some indications that residual viable tissue may be present in Q-wave-infarcted regions. Their study of 150 patients with chronic electrocardiographic Q-wave infarction found 202 dysfunctional Q-wave regions. With dobutamine stress echocardiography (DSE), they noted that 118 of these 202 regions were viable with information from the DSE testing. Construct a 90 percent confidence interval for the proportion of viable regions that one might expect to find a population of dysfunctional Q-wave regions.

Answer 1

The proportion of region expected

$p = \frac{118}{202} = 0.584 \\ n = 202$

The z score for 90% confidence level = 1.645

Confidence interval formula:

$p±Z \times \sqrt{ \frac{p(1-p)}{n} }$

The margin of error $= 1.645 \times \sqrt{ \frac{0.584 \times 0.416}{202} }=0.057$

The confidence interval = 0.584 ± 0.057

= (0.527, 0.641)