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).
To evaluate whether the proportion of female high school students who take advanced math courses in high school varies depending on the primary caregiver (father or both parents), Lilly can conduct a statistical analysis using the provided data file.
First, let's understand the variables in the data file:
- Math: This variable represents whether a student takes advanced math courses. It has two values: 0 means the student does not take advanced math, and 1 means the student takes some advanced math.
- Parent: This variable represents the primary caregiver of the high school student. It has two values: 1 means the student is primarily raised by their father, and 2 means the student is raised by both their mother and father.
To analyze this data, Lilly can perform a hypothesis test known as a Chi-Square test of independence. This test would help determine if there is a statistically significant association between the variables "Math" and "Parent."
Here's how she can perform the Chi-Square test:
1. Construct a contingency table: Lilly needs to organize the data into a contingency table, also known as a cross-tabulation table. The table will show the frequencies of the combinations of the two variables "Math" and "Parent."
2. Calculate the expected frequencies: Using the contingency table, she will calculate the expected frequencies for each cell. This step assists in comparing the observed frequencies (actual data) to the expected frequencies (what we would expect if there were no association between the variables).
3. Compute the Chi-Square statistic: To determine whether the variables "Math" and "Parent" are independent, Lilly needs to calculate the Chi-Square statistic. This statistic measures the difference between the observed and expected frequencies and provides a test statistic.
4. Determine the degrees of freedom: The degrees of freedom (df) are essential to determine the critical value from the Chi-Square distribution table. For a Chi-Square test of independence, the df is (r-1)(c-1), where "r" is the number of rows and "c" is the number of columns in the contingency table.
5. Establish the significance level: Lilly needs to decide on a significance level (alpha value) to determine the critical value from the Chi-Square distribution table. Common choices for alpha are 0.05 and 0.01.
6. Compare the Chi-Square statistic with the critical value: By comparing the Chi-Square statistic calculated in step 3 with the critical value obtained from the Chi-Square distribution table, Lilly can determine if the Chi-Square statistic is statistically significant.
7. Draw conclusions: Based on the comparison, Lilly can accept or reject the null hypothesis. If the Chi-Square statistic exceeds the critical value, Lilly can conclude that there is a significant association between the variables "Math" and "Parent." If the Chi-Square statistic does not exceed the critical value, she would fail to reject the null hypothesis, suggesting there is no significant association.
By following these steps and performing the Chi-Square test, Lilly can evaluate whether the proportion of female high school students who take advanced math courses varies depending on the primary caregiver.