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### 27 Cards in this Set

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 Define what a point estimator (estimate)is, and list two qualities that a good point estimator should have. A Point estimator (estimate) is a sample statistic that predicts the value of the parameter. A good point estimator should unbiased (centred around parameter) and efficient (low standard error). Explain what a "biased" estimator is and give an example. A biased estimator is one that, on the average, consistently over or under estimates the population parameter. Eg: in an uneven distribution, using the sample median as the estimate would be biased since the mean is skewed. True or false - the concept of bias refers only to one sample, not to the estimator's behaviour in repeated samples. False - the concept of bias in this instance refers to the estimator's behaviour in repeated samples - not just one. Why is an efficient estimator preferable? An efficient estimator, one that has as low of a standard error as possible, is preferable since, on the average, it falls closer than the other estimators to the parameter. What is the definition AF provide for an interval estimate? An interval estimate is a range of numbers around the point estimate, within which the parameter is believed to fall. A survey taken in May 1996 reported that 55% of the American public approved of President Clinton's performance in office. Is this an example of a point estimate or of the parameter? This survey is an example of a point estimate, not the parameter. Point estimates are the most common form of inference used by the mass media. R.A. Fisher made many important contributions to statistics, including a method for point estimators. What is that method calle? "Maximum likelihood estimate" What is the "Maximum Likelihood estimate"? The value of the parameter that is most consistent with the observed data in that if the parameter equaled a certain number (say 44), then the observed data has a greater chance of being 44 than any other number. Fisher showed that, for large samples, maximum likelihood estimates have three properties. List them. 1. They are efficient. 2. They have little, if any bias. 3. They are approximately normal distributions. in order for an inference to be informative it must do two things. What are they? - provide an inference about the paramter. - indicate how accurate it is. Give an example of how the point estimator depends on the characteristics of the sampling distribution. - If it is a normal distribution, than there is a high (.95) probability that the estimator falls within 2 standard deviations of the parameter. The smaller the standard error the more accurate the estimator tends to be. Define confidence interval and confidence coefficient. - Confidence interval is a range of numbers within which the parameter is believed to fall. - Confidence Coefficient is the probability that the range includes the parameter. It is close to 1, such as .95 or .99. What does the Central Limit Theorem state? That for large random samples, the sampling distribution of the mean is approximately normal. For populations over 30, what is a good substitute for the unknown standard error? A good replacement for the standard error formula is the formula s over the square root of n (s/n). What are the formulas for a 95 and 99 % confidence interval? Y +- 1.96(s) Y +- 2.58 (s) What does the error in the confidence interval refer to? List some other reasons for error. It only refers to the sampling error. Other reasons for error include non-response (refusing to answer) or measurement error (when a respondent lies). Why wouldn't a 100% Confidence Interval be employed? It is not informative. It includes all numbers from 0- infinity, so it really doesn't tell us ANYTHING. Use 99% if you must, or 95%, but not 100. What do you gain by using a 99% confidence interval, and what do you sacrifice? - You gain more assurance that it contains the parameter, but you lose presicion. Explain how you'd find out a 98% confidence interval. 1. You know that the confidence coefficient would be 1-.98=.02 2. .02 would be in both tails, so you'd divide it in 2. .02/2, which gives .01 in each tail. 3. Look up .01 in table A (that's your z-score) What is one way that a researcher can improve the precision of a confidence interval? By increasing the sample size In order to double the precision, what must one do to the sample size? Quadruple it. Quadruple the sample size to double the precision. Give one reason why the width of the confidence interval would: 1) Increase 2) Decrease The confidence interval would 1. Increase as the confidence coefficient (1-.99) increases 2. Decrease as the sample size increases. List the two things that influence the size of the sample you need. 1. Precision 2. Probability What sort of sampling types do the sample size formulas given in the text book refer to? - They are good for a) Simple random sampling and b) for systematic random sampling What is the formula given to estimate the sample size needed for a mean? N= sxs (standard dev. squared) x (z/B)squared (z/b)x(z/b). Would you need a larger sample size for a homogeneous or heterogeneous population? You'd need a larger sample size for a heterogeneous population. List five considerations in determining sample size 1. Precision 2. confidence 3. variability (in population) 4. The complexity of analysis 5. Resources (time, money etc)