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Chapter 5

# Chapter 5

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University of Toronto Scarborough

Statistics

STAB22H3

Moras

Winter

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Chapter 5 Sampling distributions of statistics provide the link between probability and data. Sampling distribution tells us about the results we are likely to see. The Distribution of a statistics A statistic from a random sample or randomized experiment is a random variable; the probability distribution of the statistic is it sampling distribution. Ex 5.1 Heights of young women We call N(64.5, 2.5) the population distribution. Population Distribution The population distribution of a variable is the distribution of its values for all members of the population. The population distribution is al the probability distribution of the variable when we choose one individual at random from the population. 5.1 Sampling distributions for counts and proportions Simplest case of a random variable has only 2 possible outcomes. N=sample size X= # of counts that represent outcome of interest Sample proportion, p-hat = Xn is used when a random variable had 2 possible outcomes. Ex: p- hat = 8402000 = 0.42 The Binomial distributions for sample counts The Binomial Setting 1. There are a fixed number n of observations. 2. The n observations are all independent. 3. Each observation falls into one of just two categories, which for convenience we call success and failure. 4. The probability of success, call it p, is the same for each observation. Ex: tossing a coin N= # of tosses Heads = success, so p is the probability of heads X= # of heads that show up Binomial Distributions The distribution of the count X of successes in the binomial setting is called the binomial distribution with parameters n and p. www.notesolution.com

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