Use The Gender And Smoke100 Pivot Table Contingency Table

Use The Gender And Smoke100 Pivot Table Contingency Table And C

Use the gender and smoke100 pivot table (contingency table) and conduct the test for independence. Are gender and having smoked at least 100 cigarettes independent? This test requires all expected values to be at least 1, are there any cells in the theoretical table that are zero? Are all the theoretical values at least 5? If so, you can make a statement about the proportions as your authors do with the gender and promotion example at the end of Chapter 1. Answer these questions using sentences and include a statement about the decision to reject or not reject the null hypothesis of independence. Use the gender and smoke100 pivot table (contingency table) to create a tree diagram using gender as the primary branch. Click into each segment and enter brief titles and values, referring to examples in the book. What other variables could be reviewed for independence in this manner, the 2 rows and 2 columns case? Conduct one such analysis, state the null and alternative hypotheses, and include the Excel tab copied from the template provided. State the decision and write what this decision means: if you reject or do not reject the null hypothesis, then what this says about the two variables. Several sentences are expected for this answer along with the completed Excel sheet.

Paper For Above instruction

The analysis of the relationship between gender and smoking behavior, specifically whether individuals have smoked at least 100 cigarettes, involves conducting a Chi-square test for independence using the provided contingency table. This test examines if the two categorical variables are independent or associated in the population. First, we analyze the observed data captured in the pivot table, ensuring that the necessary assumptions for the Chi-square test are met, particularly that all expected cell counts are at least 1 and preferably at least 5.

Calculating expected values for each cell involves multiplying the row total by the column total, then dividing by the overall total. If any expected value is zero, the Chi-square test cannot be valid because it violates the assumption that all expected counts should be greater than zero. Assuming that all expected values are at least 1 and 5, we proceed to compute the Chi-square statistic and compare it with the critical value at an appropriate significance level (commonly 0.05). The corresponding p-value determines whether we reject the null hypothesis that gender and smoking at least 100 cigarettes are independent.

Based on the computed Chi-square statistic and p-value, if the p-value is less than 0.05, we reject the null hypothesis, indicating that gender and smoking status are not independent, suggesting an association between gender and likelihood of having smoked at least 100 cigarettes. Conversely, if the p-value exceeds 0.05, we fail to reject the null hypothesis, implying no significant association and that these variables are independent in the population.

Next, a tree diagram is constructed using Word's SmartArt Graphic, illustrating gender as the primary branch that splits into segments representing male and female categories, with subsequent subdivisions or annotations reflecting the counts of individuals who have or have not smoked at least 100 cigarettes. This visual aids in understanding the distribution and relationship between these variables.

Beyond gender and smoking, other variables suitable for similar independence analyses in a 2x2 format include variables like age group versus smoking status, education level versus smoking, or income level versus smoking. For example, analyzing age groups (

• Null hypothesis (H0): Age group and smoking status are independent.
• Alternative hypothesis (H1): Age group and smoking status are associated.

An Excel spreadsheet would be prepared with observed frequencies, expected counts, and the Chi-square statistic, allowing for decision-making based on the p-value. If the test indicates a significant association, this suggests that age influences smoking behavior. Conversely, a non-significant result indicates independence, meaning age does not significantly affect smoking status within the sampled population.

References

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