Unformatted text preview: Daily sales at a pizza restaurant vary from day to day. The sales ﬁgures fluctuate around a mean . ’ p. = $900 with a standard deviation 6 = $300. What are the center and spread of the sampling distribution?
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p = $900 standarderror=3()2 =1 13 ; n=7 ( number of days per week) ". N :ﬁh‘ :‘n; : ._Iiu.._i ! E E1 owing how to ﬁnd a standard ei'ror gives us a mechanism for understanding how much variability to ‘ expectin sample statiSticslfj'tr'st by chanc=l '
> The 'dard error of the sam Ie mean = f 1' \"_"": > As the sample size n increases, the denomm or' increases, so the standard error decreases.
. , u)" With'lar’ger samplesﬁhe sample mean is more likely to fall closer to the population mean. ,"_ 5 ':l
c I  .. . o For random sampling with a large sample size n, the sampling distribution of the sample mean is
approximately a normal distribution. a This result applies no matter what the shape of the probability distribution from which the samples are taken. 0 The sampling distribution of the sample mean takes more of a bell shape as the random sample size n
increases. a The more skewed the population distribution, the larger :1 must be before the shape of the sampling
distribution is close to normal. 0 In practice, the sampling distribution is usually close to normal when the sample size n is at least about 30. o If the population distribution is approximately normal, then the sampling distribution is approximately
normal for all sample sizes. 1 ".pilnicn ismblonii: W L, L1 h: 4 {E ‘ f\ > For large n, the sampling distribution 15 approximately normal even if the population
Sundin: Disﬁturimmfi distribution is not. F /‘I ‘P This enables us to make inferences about
7‘ ' population means regardless of the shape of the population distribution.
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0:0 For large n, the sampling distribution of E is
approximately normal no matter what the shape
i I x i of the underlying population distribution. gee
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 Spring '08
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 Statistics

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