講義njue期末計量chapter3review of statistics

1、Chapter 3 Review of StatisticsQuestionsAre we worse than our parents?Are female Doctors odder than their peers?Is there glass ceiling for career women?Do mean earnings differ for men and women and, if so, by how much?Key insights of statisticsOne can learn about a population distribution by selectin

2、g a random sample from that population. Rather than survey the entire population.Statistical methodsEstimation best guessHypothesis testing formulating a specific hypothesis about the population, then using sample evidence to decide whether it is trueConfidence intervals estimating a range for an un

3、known population characteristics3.1 Estimation of the population meanSuppose you would like to know the mean value of Y in a populationEstimators the sample average or the first observationWhat makes one estimator “better” than another?unbias, consistency, and efficiencyHow to get an Estimator?3.2 H

4、ypothesis testingWhat is a hypothesis? Two-sided alternative or one-sided alternativeP-value The probability of drawing Y bar at least as far in the tails of its distribution under the null hypothesis as the sample average you actually computed.Straight-forward explanation: the probability of observ

5、ing a value of at least as different from the population mean under the null as the observed value of mean by pure random sampling variation, assuming that the null hypothesis is true.Mathematical explanation: the area in the tails of the distribution of Y bar under the null hypothesis beyond its ac

6、tual value Concludes: if p-value is small, then it is very unlikely that this sample would have been draw if null hypothesis is true, so the null hypothesis is not true, then rejected.t-statistics3.3 Confidence IntervalsUsing data from a random sample to construct a set of values that contains the t

7、rue population mean value with a certain prespecified probability. Such a set is called a confidence set, and the prespecified probability that true population mean value is contained in this set is called the confidence level. This set is all the possible values of the mean between a lower and an u

8、pper limit.3.3 Confidence Intervals How to construct a 95% confidence set?Step 1: Picking up an arbitrary value for the population meanStep 2: Testing the null hypothesis by computing the t-statistics; if it is less than 1.96, this hypothesized value is not rejected at the 5% level and write down th

9、is nonrejected value.Step 3: Now picking up another arbitrary value and repeat step 2 for all possible values3.3 Confidence Intervals Why it is useful?Confidence intervals summarize the set of hypothesis you can and cannot reject (at the x% level) based on your data3.4 Comparing Means from different PopulationsQuestion:Do recent male and female college graduates earn the same amount on average?Hypothesis Testing and Confidence intervals for the difference between two means the normal distribution: a weighted average of two normal random variables 3.7 Scatterplots, the Sa