1. In a study of heart disease in male federal employees, researchers classified 170 volunteer subjects according to their socioeconomic status (SES) and their smoking habits. SES categorized as high and low. Individuals were asked whether they were smokers or non-smoker. Here is the two way table that summarizes the data.
Smoking SES
High Low Total
Smoker 40 30 70
Non 80 20 100
Total 120 50 170
a. Determine, which hypothesis testing is appropriate to test the relationship between SES and smoking habits variable?
b. Write the HO and H1
c. Perform the test. Is there a statistically significant relationship between SES and Smoking?
PsyDAG answered a similar post. See below under "Related Questions" for the prior posting.
Joey
In how many ways can 8 students be seated in the first row in class?
40320
16777216
64
8
a. To determine which hypothesis testing is appropriate to test the relationship between the SES and smoking habits variables, we need to analyze categorical data. In this case, since we are comparing two categorical variables (SES and smoking habits) which have multiple levels, we can use the chi-square test for independence.
b. The null hypothesis (HO) for the chi-square test for independence states that there is no association between the SES and smoking habits variables, meaning that the two variables are independent. The alternative hypothesis (H1) states that there is an association between the two variables.
c. To perform the chi-square test for independence, we need to calculate the expected frequencies and the chi-square test statistic.
Step 1: Calculate the expected frequencies:
- Calculate the row totals (sum of each row) and column totals (sum of each column).
- Multiply each row total by the corresponding column total, and divide by the grand total.
Step 2: Calculate the chi-square test statistic:
- For each cell, calculate the observed frequency minus the expected frequency, squared, divided by the expected frequency.
- Sum up all these values to obtain the chi-square test statistic.
Step 3: Determine the degrees of freedom:
- Degrees of freedom = (number of rows - 1) x (number of columns - 1).
Step 4: Find the p-value:
- Use the chi-square distribution table or a statistical software to find the p-value associated with the calculated chi-square test statistic and degrees of freedom.
Step 5: Interpret the result:
- If the p-value is less than the chosen significance level (usually 0.05), we reject the null hypothesis and conclude that there is a statistically significant relationship between the SES and smoking habits variables.
- If the p-value is greater than the chosen significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant relationship between the variables.
Performing the calculations, we obtain the chi-square test statistic and the degrees of freedom, which can then be used to find the p-value. Comparing the p-value to the significance level will determine whether there is a statistically significant relationship between SES and smoking.