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	\|picture=1-PROPZINT.GIF		\|picture=1-PROPZINT.GIF
	\|summary=Computes a Z confidence interval of a proportion.		\|summary=Computes a Z confidence interval of a proportion.
	\|syntax=1-PropZInt(''x'', ''n''@@[@@, ''confidence level''@@]@@)		\|syntax=1-PropZInt(''x'', ''n''<nowiki>[</nowiki>, ''confidence level''<nowiki>]</nowiki>)
	\|location=When editing a program, press:		\|location=When editing a program, press:
	# STAT to access the statistics menu		# STAT to access the statistics menu

Maintenance script: Initial automated import

2016-02-24T18:19:10Z

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{{Template:TI-BASIC:Command
|picture=1-PROPZINT.GIF
|summary=Computes a Z confidence interval of a proportion.
|syntax=1-PropZInt(''x'', ''n''@@[@@, ''confidence level''@@]@@)
|location=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)
|compatibility=TI-83/84/+/SE
|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:

: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 =

* '''[[TI-BASIC:Errors#domain|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 =

* [[TI-BASIC:2_Propzint|2_PropZInt(]]
* [[TI-BASIC:Zinterval|ZInterval]]
* [[TI-BASIC:2_Sampzint|2_SampZInt(]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:1 Propzint - Revision history

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Maintenance script: Initial automated import