O and E stuff : Right tails only
O and E stuff : Right tails only. Use [pic]=[pic]
1.[pic]: data distributed a certain way [pic]: its not distributed that way
df=number of categories – 1
E’s are found using np where p is the probability of being in a category in Ho
2. [pic]:two characteristics are independent [pic]: they are related
df=(r-1)(c-1)
E’s are found by (row total)(column total)/(grand total)
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ANOVA: Collect data from SRS’s from S different sources. Assume the populations are normal, the variances are equal, and the data are collected independently. Then the [pic]-statistic for rejecting[pic]: All population means are equal in favor of[pic]: There is some difference in the population means is found as follows (the sums are over each of the S sources):
[pic] to find this find [pic], then [pic]this is the overall mean, [pic] is how pieces of data from source i, [pic]is the sample mean of all the data from source i, then find [pic] , then [pic], then [pic] and [pic]where[pic]is the sample variance of all the data from source i, finally [pic] The Anova Test is always a one-tail test to the right.
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Testing the population linear correlation coefficient, [pic]: use [pic]=[pic]with df = n – 2.
CI for average of all y’s with x=[pic]: [pic]
CI for a single value of y with x=[pic]: [pic]
[pic]is obtained by the regression line [pic] with [pic]in place of x.
[pic]is the critical value off the t-table with n-2 degrees of freedom.
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