Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

Of 117 randomly selected adults, 35 were found to have high blood pressure. Construct a 95% confidence interval for the true percentage of all adults that have high blood pressure.

Group of answer choices

20.1% < p < 39.8%

22.9% < p < 36.9%

19.0% < p < 40.8%

21.6% < p < 38.2%

Answer 1

Solution:

Given:

n = 117

x = 35

Thus sample proportion of adults found to have high blood pressure is:

We have to construct a 95% confidence interval for the true percentage of all adults that have high blood pressure.

Formula:

where

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

Thus