ch14estimationofmean,varianceandproportion

The results in kg are as follows the 712 600 553 654

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Unformatted text preview: timator or estimate of μ. estimate ˆ ( µ is read as μ-hat.) n Example 1: To estimate the mean weight (μ) of the of seven million residents of Hong Kong, a sample of size 8 is taken. The results (in kg) are as follows: The 71.2, 60.0, 55.3, 65.4, 32.7, 78.6, 68.8, 59.6 Estimate μ. Estimate Solution: From the 8 data we can obtain easily, ˆ µ = x = 61.45 Note: ˆ µ = x = 61.45 The estimate , computed according to (1) uses all the information in the sample fairly. There is no in­built intention to overestimate or underestimate μ. It is called an unbiased estimate for μ. unbiased To appreciate this, suppose we adopt a rule of dropping he largest value and using the average of the remaining data as an estimate for μ. ˆ Then, say, for the above data, µ = 71.2 + 60 + 55.3 + 65.4 + 32.7 + 68.8 + 59.6 = 59 Then, ˆ...
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