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C1000__22[1]

# C1000__22[1] - Inference Confidence intervals for the mean...

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1 Inference – Confidence intervals for the mean Sample mean: X Population Mean - μ

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2 Point estimate for μ: Example: Unknown: mean height of female students - μ. Estimate: We take a random sample of 225 female students and measure the mean height, , of the females in the sample. is a random variable, it may vary from sample to sample. Suppose that in a certain sample we obtained = 68 inches. X X X X
3 Limitations of point estimator - What value do we expect to get in another sample? - How reliable is this estimate? - An estimate without and indication of its variability is of little value!!! - We would like to know precisely how far tends to be from the parameter of interest μ. X X

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4 Interval estimate for μ: Specify an interval in which you think μ lies. We want to say something such as: We are 95% confident that μ is between 60 and 70 inches
5 Moreover, is approximately normal for large n (Central Limit Theorem): Therefore, according to the empirical rule (68-95-99.7): 95% interval around the mean would be within ___ standard errors around the mean X n N X σ μ , ~ 95% X n σ 2 - n σ 2 + 2 Standard error of X

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6 If the standard deviation of females heights is σ=3.0, and we take a sample of 225 - Then, a 95% interval around the mean is: For a sample mean of 68 inches: = 2 . 0
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C1000__22[1] - Inference Confidence intervals for the mean...

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