Week 4 - STAT 218 Week 4 Test Chapter 6 TEST Chapters 1-5...

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STAT 218 Week 4 Test / Chapter 6 TEST – Chapters 1-5 CHAPTER 6 – ESTIMATION AND STATISTICAL INFERENCE REVIEW STATEMENTS Recall - comment #1 We estimate unknown population parameters by sample statistics o E.g: Means for quantitative variables It is an estimate but it is not necessarily accurate How do we know HOW ACCURATE it is? How confident are we that our estimate is close? How close is it? Recall – comment #2 The standard deviation of the mean got smaller as the sample size increased. Actually by square root of n Consider the survey of the number hours per week you spent listening to music Estimate the average based upon a sample of size n = 4 If we repeated it again, we would not get the same mean. The estimate changes from sample to sample The larger the sample, the more confidence we have to estimate the population quantity This leads to the concept of a confidence interval Standard Error The standard deviation of the mean is called the Standard Error Sec section 5.3 for previous discussion Standard error = s / √n The difference between the sample mean and the population mean (µ) is rarely more than a few standard errors Reliability or precision of the estimate of the sample mean as an estimator of the population mean (µ) Standard Deviation vs Standard Error SD describes the dispersion of the data SE describes the uncertainty of the mean of the data. 1
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The Standard Error incorporates two factors that affect reliability of the estimate of the mean Inherent variability of the data (s) The sample size (n) Draw picture of s vs st.error showing change as n increases SOME CONVENIENT DEFINITIONS An estimat e is a specific value or quantity obtained for a statistic such as the mean. An unbiased estimator is one that produces an estimate that is expected to be equal to the population parameter A point estimate is a single number used to estimate a population parameter. An interval estimate is a spread or interval of values used to estimate a population parameter The confidence coefficient refers to the probability of correctly including the population parameter in the interval that is being produced. The probability is designated as “1.0 – alpha” The level of confidence is referred to as a percentage (1.0 – “alpha”) x 100% Confidence Intervals are the interval estimates based upon the confidence levels and are know as confidence limits . ESTIMATION - CONFIDENCE INTERVALS
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Week 4 - STAT 218 Week 4 Test Chapter 6 TEST Chapters 1-5...

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