Question

1. A medical institute needs information concerning cough and fever symptoms of the surrounding metropolitan population. A random sample of 420 people found that 98 had at least one of the above ailments in the past month. Find a 99% confidence interval for the population proportion that may be at risk of exhibiting similar symptoms

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 98 / 420 = 0.233

1 - = 1 - 0.233 = 0.767

Z/2 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 * (((0.233 * 0.767) / 420)

Margin of error = E = 0.053

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.233 - 0.053 < p < 0.233 + 0.053

0.180 < p < 0.286

The 99% confidence interval for the population proportion p is : 0.180 , 0.286