https://file.aiquickdraw.com/mathbot/file/1726113167331qk5y5m90.jpg

The image contains data and a statistical hypothesis test. Let's break down the key components and address the task:

### Hypotheses:
- \( H_0 \) (Null Hypothesis): The type of ticket purchased is independent of the type of flight.
- \( H_a \) (Alternative Hypothesis): The type of ticket purchased is not independent of the type of flight.

The Chi-square statistic \(\chi^2\) was computed, but the correct result is needed without rounding.

### Given Data (from the table):
- **Domestic Flights**: First Class = 29, Business Class = 95, Economy Class = 518.
- **International Flights**: First Class = 22, Business Class = 121, Economy Class = 135.

The Chi-square test statistic is calculated based on expected frequencies for each cell under the assumption that the type of ticket and type of flight are independent.

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I'll calculate the \(\chi^2\) value without rounding and provide the correct test statistic. Let's proceed with the calculations.The correct value of the Chi-square (\(\chi^2\)) test statistic, without rounding, is approximately **100.43**.

If you'd like more details about the calculations or further clarifications, feel free to ask.

Here are some related questions to deepen understanding:
1. What are the degrees of freedom for this Chi-square test?
2. How is the expected frequency calculated for each cell?
3. What does a low p-value in a Chi-square test indicate about the independence of variables?
4. How would the interpretation change if the \(\chi^2\) value were significantly lower?
5. Can you explain how the Chi-square test differs from other hypothesis tests, like t-tests?

**Tip**: Always double-check that the expected frequencies are large enough (at least 5 in each cell) to ensure the validity of the Chi-square test.

Using a 0.05 level of significance, is the type of ticket purchased independent of the type of flight? Calculate the chi-squared test statistic and p-value. Conclude based on the results.

Learn how to conduct a chi-squared test for independence using a 0.05 significance level. This example tests the independence of ticket type and flight type, calculating the chi-squared statistic and p-value. Suitable for undergraduate-level statistics students.

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