**Example:**

Find the **90% CI** for the population **proportion** of people who prefer chocolate over vanilla. Assume that your sample proportion is .67 for people who prefer chocolate. You have a sample size of 150 people.

**Solution**

What you are given from the problem:

sample size = 150

sample proportion = .67 (this is called p)

q = 1 – p = 1 – .67 = .33

NOTICE: In many textbooks, there are special symbols for the sample proportion, such as

For this example and for simplicity, I use “p” for the sample proportion and q=1 – p

The critical value or “zc” for 90% is 1.645

Why is the critical z value for a 90% Confidence Interval equal to 1.645?

Next, using the **formula** for the error **E** we have:

E = zc * sqrt [ p*q / n]

E = 1.645 * sqrt [.67 *.33/150]

E = 1.645 * sqrt(.0015)

E = 1.645 * .04

E = .07

To get the 90% Confidence Interval, we need to subtract and add E to the sample proportion.

sample prop – E < population prop < sample prop + E

.67 – .07 < population proportion < .67 + .07

.60 < population proportion < .74

The 90% Confidence Interval can also be written as:

{.60, .74}