The 1-PropZInt( Command

Command Summary

Computes a Z confidence interval of a proportion.

Command Syntax

1-PropZInt(x, n[, confidence level])

Menu Location

When editing a program, press:

  1. STAT to access the statistics menu
  2. LEFT to access the TESTS submenu
  3. ALPHA A to select 1-PropZInt(, or use arrows

(this key sequence will give you the 1-PropZInt… screen outside a program)

Calculator Compatibility


Token Size

2 bytes

The 1-PropZInt( command calculates a confidence interval for a proportion, at a specific confidence level: for example, if the confidence level is 95%, you are 95% certain that the proportion lies within the interval you get. The command assumes that the sample is large enough that the normal approximation to binomial distributions is valid: this is true if, in the sample you take, the positive and negative counts are both >5.

The 1-PropZInt( command takes 3 arguments. The first, x, is the positive count in the sample. The second, n, is the total size of the sample. (So the sample proportion is equal to x out of n). The third argument is the confidence level, which defaults to 95.

The output gives you a confidence interval of the form (a,b), meaning that the true proportion π is most likely in the range a<π<b, and the value of x/n.

Sample Problem

You want to know the proportion of students at your school that support a particular political candidate. You take a random sample of 50 students, and find that 22 of them support that candidate. 22, the positive count, and 50-22=28, the negative count, are both >5, so the assumption is satisfied.

Using 22 for x, and 50 for n, you decide to find a 95% confidence interval. The syntax for that is:

which can also be

The output if you run the above code will look approximately like this:

This tells you that between about 30.2% and about 57.8% of the students at your school are in support of the political candidate.


If the confidence level is 95%, you can omit the final 95, since that is the default value:

can be

Error Conditions

  • ERR:DOMAIN is thrown if the sample proportion is not between 0 and 1, any argument is negative, or the confidence level is 100 or more.

Related Commands


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