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Lecture 7

Lecture 7 - October 31.

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Damian Dupuy

October 31 – Lecture 7 Confidence Intervals IV (IMPORTNAT FOR EXAM) ________________________________________ 1-a a a/2 Za/2 .90 .10 .05 1.645 .95 .05 .025 1.96 .98 .02 .01 2.33 .99 .01 .005 2.58 (a – isAlpha) Example – to say We are 95% or watever confident that our sample will fall in the following range – For 95% confidnent there is 5% chance it wont be – If we undertook a sample, --> 95% will contain population Parameter and 5% of them wont When dealing with Sampling distribution – the numbers above are the ones that are always needed and be used. If we have a 95% confidence then there is 5% significance Choosing Correct Sample Size – The only way we could have it all – high level of confidence and high level of precision is to increase the number of sample size – it gets steaper , the small distribution around the mean – therefore, the smaller the number of error . – Therefore we could be more precise in our – How prices/close – accuracy means --> does our sample actually reflect the – how close our smaple really easy to our population sample. ??? not sure - Total amount of information is due to: – Sampling design used – Sample size n – the bigger the sample – the more information about the population it will tell – But, how many observations should be included in the sample? – Greater or equal to 30 – the more the better – Have to consider the relationship between the width of the interval and the level of confidence – the width increases and we have to be concerned about it – increasing of interval width, increases confidence – but decreases precision – Only way to increase confidence without increasing the width, is to increase sample size – to have a small interval and have a high confidence, increase the SAMPLE*** Chosing Correct Sample Size II – Taking a sample larger than necessary wastes time and effort (very costly) – Factors to consider are: – Type of sample i.e. Random, Stratified etc. – Population parameter being estimated – is it the mean or std deviation ?? – Degree of Precision (width of confidence interval) – Level of Confidence – what level of confidence do i require and what level i will be testing – the only way to increase to confidence and decrese the width is to increase sample – At a particular confidence level, increasing the sample size provides greater precision, and narrows the confidence interval Choosing Correct Sample Size III (CHECK BOOK) Za/2 S n = ( E )2 Where E is the amount of sampling error the researcher is wiling to tolerate For Data measured in proportions, the formula is ... ____ Za/2 /pq n= ( E )2 EXAMPLE: 1. Urban planner wants to estimate the mean number of people per household 2. Using 90% confidence level, and stating that their estimate will be within .3 persons of the true population mean. 3. S is determined through pre-sampling to be 1.25 4. What is the minimum number of households that must be sampled? Using formula Za/2S (1.65) (1.25) n = ( E )2 ---> n= ( .3 )2 = 47.26 or 48 households Therfore, he/she needs a random sample of, at least 48 households to ensure that level of precision at the 90% confidence level. Estimation – Small Samples – When n
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