Question

5) It is felt that first-time heart attack victims are particularly vulnerable to additional heart attacks during the year following the first attack. To estimate the proportion of first-time heart attack victims who suffer an additional attack within one year, a random sample of 300 first-time heart attack patients of Medical College of Georgia was tracked for one year.

a) If 254 of the 300 sampled did not suffer an additional heart attack within one year, construct a 95% confidence interval of the population proportion of first-time heart attack patients of Medical College of Georgia who suffer an additional attack within one year provided it is valid.

(5 points)

b) Find a point estimate for the population proportion of first-time heart attack patients of Medical College of Georgia who do not suffer an additional attack within one year. (1 point)

c) Suppose 20% of the first-time heart attack patients of Medical College of Alabama suffer an additional attack within one year. Based on your confidence interval in part a), is the proportion of first-time heart attack patients who suffer an additional attack within one year in Medical College of Georgia the same as that of Alabama (0.20) ? Why or why not? (2 points)

d) How many first-time heart attack victims need to be sampled so as to estimate the population proportion of them who suffer an additional attack within one year with a 92% confidence? The point estimate must be within 3.6% of the true population proportion and no preliminary estimates are available. (4 points)

Answer 1

a) If 254 of the 300 sampled did not suffer an additional heart attack within one year, construct a 95% confidence interval of the population proportion of first-time heart attack patients of Medical College of Georgia who suffer an additional attack within one year provided it is valid.

(5 points)

The confidence interval for the proportion is obtained using the formula,

Where,

b) Find a point estimate for the population proportion of first-time heart attack patients of Medical College of Georgia who do not suffer an additional attack within one year. (1 point)

c) Suppose 20% of the first-time heart attack patients of Medical College of Alabama suffer an additional attack within one year. Based on your confidence interval in part a), is the proportion of first-time heart attack patients who suffer an additional attack within one year in Medical College of Georgia the same as that of Alabama (0.20) ? Why or why not? (2 points)

The 95% confidence interval of the population proportion of first-time heart attack patients of Medical College of Georgia who suffer an additional attack within one year is (11.3%,19.4%)

while 20% of the first-time heart attack patients of Medical College of Alabama suffer an additional attack within the one-year which is outside and greater than the 95% confidence interval for Medical College of Georgia. Hence the proportion for Medical College of Georgia is not the same as that of Alabama

d) How many first-time heart attack victims need to be sampled so as to estimate the population proportion of them who suffer an additional attack within one year with a 92% confidence? The point estimate must be within 3.6% of the true population proportion and no preliminary estimates are available.

The sample size is obtained using the formula,

Where,

Let  

Now,