From the image provided, this is a chi-squared test of independence problem, where you need to test if the car model and package options are independent using the given data.

Here's how you proceed:

1. Set Up Hypotheses:

   • Null Hypothesis ($H_0$): The model and package options are independent.
   • Alternative Hypothesis ($H_1$): The model and package options are not independent.

2. Degrees of Freedom:

   • Formula: $df = (rows - 1) \times (columns - 1)$
   • With 4 models and 3 packages: $df = (4 - 1) \times (3 - 1) = 3 \times 2 = 6$.

3. Expected Values:

   • Calculate the expected frequencies for each cell using the formula: $E_{ij} = \frac{(row \ total) \times (column \ total)}{grand \ total}$

4. Chi-Square Test Statistic ($\chi^2$):

   • Formula: $\chi^2 = \sum \frac{(O_{ij} - E_{ij})^2}{E_{ij}}$ where $O_{ij}$ is the observed frequency.

5. P-Value:

   • Use a chi-squared distribution table or calculator to find the p-value based on the calculated $\chi^2$ and $df = 6$.

Once you compute the test statistic and p-value, compare the p-value with the significance level ($\alpha = 0.05$) to determine whether to reject $H_0$.

Would you like me to calculate the expected values, $\chi^2$, and p-value for you? Let me know!

1. What are the steps to compute expected frequencies for this test?
2. How do degrees of freedom impact the chi-squared distribution?
3. Why is a significance level (e.g., 0.05) essential in hypothesis testing?
4. What does rejecting $H_0$ imply about the independence of variables?
5. How is the p-value interpreted in the context of hypothesis testing?

Tip: Always double-check observed and expected values to avoid errors in chi-square calculations.