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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 245 305 200 265 180 222 150 228 775 1020

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Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

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Chapter
Section
BuyFindarrow_forward

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 10, Problem 10.13P
Textbook Problem
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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
245 305 200 265 180 222 150 228 775 1020

To determine

To find:

The chi square value for the given information and test for its significance.

Explanation of Solution

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 fe is given as,

fe=Rowmarginal×ColumnmarginalN

Where N is the total of frequencies.

The chi square statistic is given by,

χ2(obtained)=(fofe)2fe

Where fo is the observed frequency,

And fe is the expected frequency.

The degrees of freedom for the bivariate table is given as,

df=(r1)(c1)

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,

fe=Rowmarginal×ColumnmarginalN……(1)

Substitute 245 for row marginal, 305 for column marginal and 1020 for N in equation (1).

f1=245×3051020=73.26

Substitute 245 for row marginal, 265 for column marginal and 1020 for N in equation (1).

f2=246×2651020=63.65

Substitute 245 for row marginal, 222 for column marginal and 1020 for N in equation (1).

f3=245×2221020=53.32

Substitute 245 for row marginal, 228 for column marginal and 1020 for N in equation (1).

f4=245×2281020=54.76

Substitute 775 for row marginal, 305 for column marginal and 1020 for N in equation (1).

f5=775×3051020=231.74

Substitute 775 for row marginal, 265 for column marginal and 1020 for N in equation (1).

f6=775×2651020=201.35

Substitute 775 for row marginal, 222 for column marginal and 1020 for N in equation (1).

f7=775×2221020=168.68

Substitute 775 for row marginal, 228 for column marginal and 1020 for N in equation (1).

f8=775×2281020=173.24

Consider the following table,

fo fe fofe (fofe)2 (fofe)2/fe
60 73

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