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Chapter 7 - Sampling Distributions (2)

# Chapter 7 - Sampling Distributions (2) - m Given that the...

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Unformatted text preview: m Given that the exit poll had 2705 people and assuming 50% support the reelection of Schwarzenegger. Find the _- ' , .. ' - o -ualtion nrmnortio and ,1 ; standard error: population proportion = p = .5 7 ' ’ ‘ p(l—p) = .5(1—.5) =_0096 _- n 2705 .9 tan dard error = a = (1) _This is the probability distribution from which we take the sample. Values of its parameters are usually unknown. They’ re what we’d like to learn about (2) m: This is the distribution of the sample data. It’s the distribution we actually see in practice. It’s described by statistics. With random sampling, the larger the sample size n, the more closely the data distribution resembles the population distribution (3)_I'his is the probability distribution of a sample statistic. With random sampling, the sampling distribution provides probabilities for all the possible values of the statistic. The sampling distribution provides the key for telling us how close a sample statistic falls to the corresponding unknown parameter. Its standard deviation is called the standard error. Example 3: Consider the distribution of sample mean ages in Example 1 Possible values for the random variable (sample mean age ( i )) are 27, 28, 29, 30, and 31 W Population mean age: (27+33+30+24+30)/5 = 28.8 I n-nnmma 2/10 3/10 2/10 1/10 Mean of the sampling distribution _ _ i 2 3 Mean - ExPOr) — (27 x 10) + (28 x 101+ (29 x —) + (30x12 —)+(31x—-) = 28.8 moan > The sample mean, i, is a random variable. > The sample mean varies from sample to sample. > By contrast, the population mean, u, is a single ﬁxed number. ill - > For a rdoman samp {omen : oma population having mean u and standard deviation 0, the sampling distribution of the sample mean has: nudescribed by the mean u (the same as the mean of the population). owescribed by the standard error, which equals the population st square root of the -.... standard error of f = a/J; i viat' ' ' edb the who distribﬁm for wrangle opus/110v? WWP . S—rqndﬂwl mar: £23.). ...
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