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STAT212

# STAT212 - MOE does not accommodate errors due to sampling...

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Inference- help distinguish patterns seen in data between those that are due to chance and those that reflect a real feature of the phenomenon under study. Does the mean actually conclude a feature of the sample or is this based on chance/variation. A confidence interval supplements an estimate of a parameter with an indication of its variability. A 95 % interval means that the population mean will lie within the sample mean for 95 % of the samples. The confidence level for x^ within a(sx) units from u is C= P(-a[sx] </ x^ - u </ a[sx]) e.g. x^ +- a(sx). This is known as the margin of error (half the length of the interval) If the confidence interval is given, CI= x^ +- z*[sd/sqroot(n)] where z* is the critical value. The corresponding margin of error is m= z*(sd/srootn). Hence increasing confidence level or decreasing sample size, increases MOE. The
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Unformatted text preview: MOE does not accommodate errors due to sampling bias. A sample size may be chosen to target a desired MOE. n= (z*sd/m)^2. If n=103.2, then you take 104. Hypothesis or significance test assesses the truth of a hypothesis about a parameter by comparing it with observed data. Ho- Null hypothesis; status quo in terms of the parameter. Ha- Alternative hypothesis; suspicion (could be greater than, less than [one sided], or not equal to Ho. [two sided]) Select a test statistic x^ and calculate P-value- measures the compatibility of the data with Ho. The smaller the P-value, the stronger the evidence in favor of Ha. The p value is normsdist of the z value. The distance from x^ to Ho is in units of sd. Compare the P-value to the desired significance level in order to conclude....
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