If We Suspect That There Is No Relationship Between Gender

If We Suspect That There Is No Relationship Between Gender And Support

If we suspect that there is no relationship between gender and support of legalizing marijuana, what would be the best alternative hypothesis? A. There is a relationship between gender and support of legalizing marijuana. B. Gender has no influence on support of legalizing marijuana. C. There is a relationship between gender and marijuana use. D. Not enough data.

Which of the following is the correct degrees of freedom in the table below? A. 4 B. 3 C. 2 D. 1

What is our critical value for our degrees of freedom in the above-referenced table if the alpha level is set at .05? The decision rule is that if X² > this number, the null hypothesis will be rejected. A. 5.99 B. 3.841 C. 2.71 D. 4.35

Given the above information, we fail to reject the null hypothesis (or simply accept that the null hypothesis is true in the current case). A. True B. False

Paper For Above instruction

The relationship between gender and attitudes toward the legalization of marijuana is a pertinent subject in public health and social policy research. To analyze whether a significant association exists, statistical hypotheses testing, particularly the chi-square test of independence, is employed. This paper discusses the formulation of hypotheses, the determination of degrees of freedom, critical values for significance testing, and the interpretation of results in the context of testing the independence between gender and support for marijuana legalization.

When investigating whether gender influences support for legalizing marijuana, the null hypothesis (H₀) stipulates no association between these variables, meaning gender and support are independent. Conversely, the alternative hypothesis (H₁) posits that a relationship does exist, indicating dependency between gender and attitudes toward legalization. Based on the question, the best alternative hypothesis would be that there is a relationship between gender and support for legalization (option A). This aligns with standard hypothesis testing where the null suggests no association, and the alternative indicates an existing relationship.

The degrees of freedom (df) for a chi-square test of independence in a contingency table depend on the number of categories in each variable. If the table used to analyze gender (with two categories: male and female) and support (yes or no), then the degrees of freedom are calculated as (rows - 1) × (columns - 1). Given two categories for each variable, the degrees of freedom are (2 - 1) × (2 - 1) = 1 × 1 = 1, making option D the correct choice in the context. However, if the table has more than two categories, the options would change accordingly.

The critical value at the 0.05 significance level depends on the degrees of freedom. For df = 1, the chi-square critical value from the chi-square distribution table is approximately 3.841. This means that if the computed chi-square statistic exceeds this value, we reject the null hypothesis. Thus, for degrees of freedom of 1 at α = 0.05, the critical value is 3.841, making option B the correct answer for the critical value. All other options pertain to different df values or significance levels.

Finally, if the computed chi-square statistic does not exceed the critical value, we fail to reject the null hypothesis, suggesting insufficient evidence to conclude an association exists between gender and support for marijuana legalization. In this context, the statement that we fail to reject the null hypothesis is true if the test statistic is less than or equal to the critical value, supporting option A ("True"). This indicates that based on the data, there is no statistically significant relationship between gender and the support of legalizing marijuana.

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