To calculate a proportion from a single sample:

= count of “successes” in sample sample size (n)

Sample ProportionsA percent out of the total sample that

responds a particular way.

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In a study of people’s favorite fast food restaurants, 235 people said they prefer Zaxby’s out of the 672 people that were surveyed. What proportion of the people surveyed

claimed they preferred Zaxby’s?

Central Limit Theorem for Proportions

For multiple samples each of size n, if AND , then a Normal approximation can also be used for the distribution of proportions.

Once CLT applies, we can then use any sample proportion and a desired confidence level to estimate the TRUE PROPORTION for the entire population.

Sample proportion

TRUE proportion will fall somewhere within this interval

 

Confidence Interval Formula for Proportions

Using the proportion of the sample that preferred Zaxby’s, create a 90% confidence interval for the proportion of all people that prefer Zaxby’s.