Question

A study found that of 3,532 randomly selected Americans with hypertension, only 1,219 were receiving treatment for it.

A. What is the sample statistic (p̂ or ȳ)? Please calculate/write its value.

B. Construct a 90% confidence interval for the true proportion of all Americans who are having their hypertension treated. Provide the interval in (left endpoint, right endpoint) format.

C. Interpret the confidence interval in the context of the study.

Answer 1

Solution :

n = 3532

x = 1219

a ) = x / n =1219 / 3532 = 0.345

1 - = 1 - 0.345 = 0.655

b ) At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * (((0.345 * 0.655) / 3532 )

= 0.013

c ) A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.345 - 0.013 < p < 0.345 + 0.013

0.332< p < 0.358

The left endpoint = 0.332

The right endpoint =0.358