Lilly collects data on a sample of 40 high school students to evaluate whether the proportion of female high school students who take advanced math courses in high school varies depending upon whether they have been raised primarily by their father or by both their mother and their father. Two variables are found below in the data file: math (0 = no advanced math and 1 = some advanced math) and Parent (1= primarily father and 2 = father and mother).
Parent Math
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
1.0 0.0
2.0 0.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 1.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
2.0 0.0
a) Conduct a crosstabs analysis to examine the proportion of female high school students who take advanced math courses is different for different levels of the parent variable.
b) What percent female students took advanced math class
c) What percent of female students did not take advanced math class when females were raised by just their father?
d) What are the Chi-square results? What are the expected and the observed results that were found? Are they results of the Chi-Square significant? What do the results mean?
e) What were your null and alternative hypotheses? Did the results lead you to reject or fail to reject the null and why?
a) To conduct a crosstabs analysis, you can use a statistical software like SPSS or Excel. In this analysis, you want to examine the proportion of female high school students who take advanced math courses for different levels of the parent variable. The parent variable categorizes whether the student was primarily raised by their father (1) or both their mother and father (2). The math variable categorizes whether the student took advanced math (1) or not (0).
To perform the crosstabs analysis:
1. Open the dataset in your preferred statistical software.
2. Select the crosstabs or contingency table analysis function.
3. Choose the parent variable as the row variable and the math variable as the column variable.
4. Run the analysis and review the results. This will provide you with the proportion of female high school students who took advanced math courses for each level of the parent variable.
b) To calculate the percentage of female students who took advanced math class, you need to find the total number of female students who took advanced math (1) and divide it by the total number of female students. From the provided data, we can see that 12 female students took advanced math. To find the total number of female students, add up the number of females in the 'Parent' variable.
Total number of female students who took advanced math = 12
Total number of female students = 12 + 10 (from the 'Parent' variable)
Percentage of female students who took advanced math = (12 / (12 + 10)) * 100
c) To calculate the percentage of female students who did not take advanced math class when raised by just their father, you need to find the number of female students who did not take advanced math (0) when the 'Parent' variable is 1 (primarily father). In the provided data, we can see that 11 female students were raised primarily by their father and did not take advanced math.
Number of female students raised primarily by father who did not take advanced math = 11
Total number of female students raised primarily by father = 11 + 10 (from the 'Parent' variable)
Percentage of female students raised primarily by father who did not take advanced math = (11 / (11 + 10)) * 100
d) To obtain the Chi-square results, you need to use a statistical software that can conduct the Chi-square test. This will give you the expected and observed results, as well as the significance of the Chi-square test.
Expected results: These are the expected frequencies calculated based on the assumption that there is no association between the parent variable and the math variable.
Observed results: These are the actual frequencies observed in the data.
Chi-square significance: The Chi-square test calculates the p-value, which measures the significance of the association between the two variables. If the p-value is below a predetermined significance level (usually 0.05), it indicates that the association between the variables is statistically significant.
The results of the Chi-square test will help determine if there is a significant association between the proportion of female high school students who take advanced math courses and the level of the parent variable.
e) The null hypothesis (H0) in this case is that there is no association between the proportion of female high school students who take advanced math courses and the level of the parent variable. The alternative hypothesis (Ha) is that there is an association between these two variables.
Based on the Chi-square results and the significance level (p-value), you can either reject or fail to reject the null hypothesis. If the p-value is below the significance level, you reject the null hypothesis, indicating that there is a significant association between the variables. If the p-value is above the significance level, you fail to reject the null hypothesis and conclude that there is no significant association between the variables.