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).
Data missing.
To analyze this data and determine if the proportion of female high school students who take advanced math courses varies depending on whether they were raised primarily by their father or both their mother and father, you can perform a statistical test called a chi-square test for independence. This test evaluates whether there is a relationship between two categorical variables.
To conduct this test, you would follow these steps:
1. State the null and alternative hypotheses:
- Null hypothesis (H0): There is no association between the proportion of female high school students taking advanced math courses and the type of parental upbringing (father or both parents).
- Alternative hypothesis (Ha): There is an association between the proportion of female high school students taking advanced math courses and the type of parental upbringing.
2. Set the significance level (alpha):
- The significance level, denoted as α, determines the threshold for deciding the statistical significance of the results. It is usually set to 0.05 (5%).
3. Create a contingency table:
- A contingency table is used to summarize the data and compare the observed frequencies with the expected frequencies under the null hypothesis. You would count the number of female students for each category of the Parent variable and the number of females taking advanced math courses (coded as 1) and not taking advanced math courses (coded as 0).
4. Calculate the expected frequencies:
- Under the null hypothesis, the expected frequencies are calculated based on the assumption that there is no association between the two variables. The expected frequency for each cell of the contingency table can be computed by multiplying the marginal totals (row total and column total) and dividing by the total sample size.
5. Compute the test statistic:
- The chi-square test statistic measures the discrepancy between the observed and expected frequencies in each cell of the contingency table. It is calculated by summing the squared differences between the observed and expected frequencies, divided by the expected frequencies.
6. Determine the critical value or p-value:
- The critical value is obtained from the chi-square distribution table based on the degrees of freedom (df) and the chosen significance level. Alternatively, you can calculate the p-value using statistical software or online calculators. The p-value represents the probability of obtaining the observed test statistic (or more extreme) under the null hypothesis.
7. Compare the test statistic with the critical value or p-value:
- If the test statistic is greater than the critical value (or if the p-value is less than the significance level), the null hypothesis is rejected. This would indicate that there is evidence of an association between the two variables.
8. Interpret the results:
- If the null hypothesis is rejected, it implies that the proportion of female high school students taking advanced math courses varies depending on the type of parental upbringing. The specific nature of the association can be explored further using additional statistical methods or visualization techniques.
Please note that the exact steps and formulas for conducting the chi-square test for independence may vary slightly depending on the statistical software or tool you are using.