In: Statistics and Probability
A study found that of 3,532 randomly selected Americans with hypertension, only 1,219 were receiving treatment for it.
1.What is the sample statistic (p̂ or ȳ)? Please calculate/write its value.
2.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.
3.Interpret the confidence interval in the context of the study.
Solution :
n = 3532
x = 1219
= x / n = 1219/ 3532 = 0.345
1 - = 1 - 0.345 = 0.655
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.576* (((0.345 * 0.655) / 3532)
0.021
A 99 % confidence interval for population proportion p is ,
- E < P < + E
0.345 - 0.021 < p < 0.345 + 0.021
0324 < p < 0.366
Left endpoint =0.324
Right endpoint =0.366