Computes a Z confidence interval of a proportion.

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

When editing a program, press:

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

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

TI-83/84/+/SE

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:

```
: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.

# Related Commands

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