Math Problem Statement

A magazine subscriber study asked, "In the past 12 months, when traveling for business, what type of airline ticket did you purchase most often?" A second question asked if the type of airline ticket purchased most often was for domestic or international travel. Sample data obtained are shown in the following table. Type of Ticket Type of Flight Domestic International First class 29 22 Business class 93 119 Economy class 520 137 (a) Using a 0.05 level of significance, is the type of ticket purchased independent of the type of flight? State the null and alternative hypotheses.

H0: The type of ticket purchased is independent of the type of flight. Ha: The type of ticket purchased is not independent of the type of flight. H0: The type of ticket purchased is mutually exclusive from the type of flight. Ha: The type of ticket purchased is not mutually exclusive from the type of flight.
H0: The type of ticket purchased is not mutually exclusive from the type of flight. Ha: The type of ticket purchased is mutually exclusive from the type of flight. H0: The type of ticket purchased is not independent of the type of flight. Ha: The type of ticket purchased is independent of the type of flight. Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion.

Do not reject H0. We cannot conclude that the type of ticket purchased and the type of flight are not independent. Reject H0. We conclude that the the type of ticket purchased is not independent of the type of flight.
Do not reject H0. We cannot conclude that the type of ticket purchased and the type of flight are independent. Reject H0. We conclude that the type of ticket purchased is independent of the type of flight. (b) Discuss any dependence that exists between the type of ticket and type of flight.

A higher percentage of first class and business class tickets are purchased for domestic flights compared to international flights. Economy class tickets are purchased more for international flights. The type of ticket purchased is independent of the type of flight.
A higher percentage of first class and business class tickets are purchased for international flights compared to domestic flights. Economy class tickets are purchased more for domestic flights. A lower percentage of economy class tickets are purchased for domestic flights compared to international flights. First class and business class tickets are purchased more for domestic flights.

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Hypothesis Testing
Chi-square Test of Independence

Formulas

Chi-square test statistic: χ² = Σ((O_ij - E_ij)² / E_ij)
Expected frequency: E_ij = (Row Total × Column Total) / Grand Total
p-value

Theorems

Chi-square Test of Independence

Suitable Grade Level

Undergraduate (Statistics Course Level)