Question

Of 110 randomly selected adults, 35 were found to have high blood pressure.
a.Construct a 90% confidence interval for the true percentage of all adults that have high blood pressure.

b.Write a statement explaining your confidence interval.

Answer 1

Solution :

n =110

x = 35

= x / n = 35 / 110 = 0.318

1 - = 1 - 0.318 = 0.682

a ) 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 * (((0.318 * 0.682) / 110)

= 0.073

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

- E < P < + E

0.318 - 0.073 < p < 0.318 + 0.073

0.245 < p < 0.391