# STA 2023 Lecture Notes - Lecture 2: Central Limit Theorem, Binomial Distribution, Statistic

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➔ what sampling distribution do we use if we have quantitative data?

quantitative

➔ what sampling distribution do we use if we have categorical data?

qualitative

➔ what does p-hat estimate in a sample proportion?

population proportion

➔ what are possible values of p-hat?

0-1

➔ what is the purpose of a sampling distribution?

see the pattern when we take many samples and compute the sample statistic

for each

➔ why are statistics random variables?

they come from random samples

➔ what is the distribution of a statistic called?

sampling distribution

➔ does p-hat have a binomial distribution?

never

➔ what is the mean of the distribution of p-hat?

p

➔ what is the standard error of the distribution of p-hat?

sq rt (p(1-p)/n)

➔ conditions for sampling distribution of p-hat

p≥ 15 AND n(1-p) ≥ 15

➔ what does x-bar estimate?

μ

➔ what represents the true proportion of successes in the entire population (a

parameter)?

p

➔ what represents the proportion of successes computed for the sample (a statistic

or estimator)?