Chapter 11. Chi-Square and F Distributions. Understandable Statistics Ninth Edition By Brase and Brase Prepared by Yixun Shi Bloomsburg University of Pennsylvania. The Chi-Square Distribution. The χ 2 distribution has the following features: All possible values are positive.
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H0: The variables are independent
H1: The variables are not independent
O = the observed frequency in each cell
E = the expected frequency in each cell
n = the total sample size
Obtain random samples from each of the population. For each population, determine the numbers that share a distinct specified characteristic. Make a contingency table with the different populations as the rows (or columns) and the characteristics as the columns (or rows). The values recorded in the cells of the table are the observed value O taken from the samples.
H0: The proportion of each population sharing specified characteristics is the same for all populations.
H1: The proportion of each population sharing specified characteristics is not the same for all populations.
2. Follow steps 2—5 of the procedure used to test for independence.
H0: The population fits the given distribution.
H1: The population has a different distribution.
has a chi-square distribution with n – 1 degrees of freedom.
Use Table 7 in Appendix II.
Confidence Intervals for σ
We will compare the test statistic to an F distribution, found in Table 8 of Appendix II.
Estimate the P-Value for F = 55.2 with d.f.N = 3 and d.f.D = 2
In ANOVA, there are k groups and k group means.
The general problem is to determine if there exists a difference among the group means.