Ch 12: Sampling Distributions & Normal Deviate test

1. Introduction





2. Sampling Distribution of a statistic defined:

a sampling distribution of a statistic gives 1) all the values that the statistic can take and

2) the probability of getting each value under the assumption that the value occurred by chance.





A. Sign test







B. Generating a sampling distribution of the mean

Example: Given the population scores of 3,4,5,6,7 determine the sampling distribution of the mean for N=2. Assume sampling with replacement.









C. Characteristics of the sampling distribution of the mean.












3. The normal deviate test



A. probability of sampling a value from the normal distribution





B. The normal deviate test








C. Evaluating the statistic using "critical region"





1. critical region: there is a region under the curve that contains all the values of the statistic that allow for rejection of the null.



i. If zobt falls within the critical region



ii. What is this region? It is determined by alpha





iii. Where does this region begin? It is determined by the critical value of the statistic, ie., the value that bounds this region.





2. An economist wants to know if mean income has changed in ND over the last decade. In 1980 the values were mew=$10,000 and sd = 1500. She took a sample of 250 citizens and found a mean income of 9623. What should she conclude?

Step 1: What are the hypotheses





step 2: find zobt



step 3: find zcrit



step 4: is |zobt| >= zcrit? If so reject null

4. Power and the normal deviate test.



A. Power





B. Steps





2.





Statistics