NOTES_Lecture 23-24_Estimation

NOTES_Lecture - • It is consistent but it is biased Sample mean diff btw sample means and sample proportion are consistent(and unbiased o

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11/10/11 Lecture 22: Sampling Proportions NOTE ON QUIZ 4 - Be an expert on sampling distribution for the upcoming test X and Y parameters are both binomially distributed (with replacement) Slide 12, this binomial distribution fails the rule of thumb o Can’t use the normal approximation to measure binomial probability o Sample proportion Lecture 23: Estimation The population is not bell shaped, it is symmetric o Point estimate of is 7 o 90% interval estimate of 90% of observations lie within .623 and 13.16 Determine std. dev of sample mean by dividing by sq. rt. of observations Should the sampling distribution of the sample mean should be bell-shaped Estimator Properties o Unbiasedness On average (in expectation) gives you the right answer May have sampling noise, but not biased o Direction of Bias Expected value of sampling error is zero Sample range will always be smaller than expectation range, it is a downward bias o Consistency Sample range increases as sample size increases
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Unformatted text preview: • It is consistent but it is biased Sample mean, diff. btw sample means, and sample proportion are consistent (and unbiased?) o Relative Efficiency Theta is a generic population parameter/sample statistic – the general case has less sampling error than Both are unbiased, but sample mean has less sampling error than the sample median Sample mean is more efficient Lecture 24: Estimation: Estimating when Known • Example o Might want to know mean of survey and variability in population • N is greater than 30, should be a bell curve o Best estimate of sample mean, but could be smaller, could be bigger • Alpha – convention is .05 – 95% sure • Un-Standardize , we do assume that the Central Limit Theorem still applies • Income Example o 95% sure that the mean will be between the two numbers • Interval and its Interpretation o X-bar is variable so it would affect interpretation, the interval is random •...
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This note was uploaded on 11/09/2011 for the course ECO 220 taught by Professor Tanaka during the Fall '11 term at University of Toronto- Toronto.

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