Property	Value
Hex Value	`$BB43`
Categories	Catalog > P Statistics > Operations
Localizations	FR: `1-PropZInt(`

`1-PropZInt(`

Overview

Computes a one-proportion z confidence interval.

Availability: Token only available from within the Basic editor.

Syntax

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

Arguments

Name	Type	Optional
x
n
confidence level		Yes

Location

stat, TESTS, A:1-PropZInt(

Description

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:

:1-PropZInt(22,50,95
which can also be
:1-PropZInt(22,50,.95

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

1-PropZInt
 (.30241,.57759)
 p=.44
 n=50

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.

Optimization

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

:1-PropZInt(22,50,95
can be
:1-PropZInt(22,50

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.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

History

Calculator	OS Version	Description
TI-83	0.01013	Added

Authors: Adrien Bertrand

1-PropZInt(