Does support for the legalization of marijuana vary by region of the country? The table displays the relationship between the two variables for a random sample of 1020 adult citizens. Is the relationship significant? Describe the pattern of the relationship, using column percentages. Which region is most in support of legalization?
Legalize?  Region  
North  Midwest  South  West  Totals  
Yes  60  65  42  78  245 
No Totals 





To find:
The chi square value for the given information and test for its significance.
Given:
The given statement is,
Does support for the legalization of marijuana vary by region of the country? The table displays the relationship between the two variables for a random sample of 1020 adult citizens.
The given table of information is,
Legalize?  Region  Totals  
North  Midwest  South  West  
Yes  60  65  42  78  245 
No  245  200  180  150  775 
Totals  305  265  222  228  1020 
Approach:
The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.
The five step model for hypothesis testing is,
Step 1. Making assumptions and meeting test requirements.
Step 2. Stating the null hypothesis.
Step 3. Selecting the sampling distribution and establishing the critical region.
Step 4. Computing test statistics.
Step 5. Making a decision and interpreting the results of the test.
Formula used:
For a chi square, the expected frequency
Where N is the total of frequencies.
The chi square statistic is given by,
Where
And
The degrees of freedom for the bivariate table is given as,
Where r is the number of rows and c is the number of columns.
Calculation:
From the given information,
The observed frequency is given as,
Substitute 245 for row marginal, 305 for column marginal and 1020 for N in equation
Substitute 245 for row marginal, 265 for column marginal and 1020 for N in equation
Substitute 245 for row marginal, 222 for column marginal and 1020 for N in equation
Substitute 245 for row marginal, 228 for column marginal and 1020 for N in equation
Substitute 775 for row marginal, 305 for column marginal and 1020 for N in equation
Substitute 775 for row marginal, 265 for column marginal and 1020 for N in equation
Substitute 775 for row marginal, 222 for column marginal and 1020 for N in equation
Substitute 775 for row marginal, 228 for column marginal and 1020 for N in equation
Consider the following table,
60  73 
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