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 fordomestic or international travel. Sample data obtained are shown in the following table.Type of TicketOFirst classBusiness classEconomy classDomestic29Type of Flight99=514International22125(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.O Ho: 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.131Ho:: The type of ticket purchased is not mutually exclusive from the type of flight.H₂: The type of ticket purchased is mutually exclusive from the type of flight.O Ho: 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.O Ho: 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

For testing whether the type of tickets purchased is independent of the type of flight, the observed data is given as:Type of ticketType of flightDomesticInternationalFirst class2922Business class99125Economy class514131Level of significance:The null hypothesis is the statement which is tested for the possible rejection.Therefore, in the given case, we assume the null hypothesis as the type of ticket purchased is independent of type of flight.The alternative hypothesis is the statement which contradicts the null statement and is supporting the claim to be assumed.Therefore, the alternative hypothesis is assumed as the type of ticket purchased is not independent of type of ticket.The third option correctly matches with both the statements for null and alternative hypotheses as:The type of ticket purchased is independent of type of flight.The type of ticket purchased is not independent of type of ticket.First ,second and fourth options are incorrect as they do not correctly matches with the obtained statements for null and alternative hypotheses.The observed frequencytheses O subscript i close parentheses" role="math" style="max-width: none; vertical-align: -9px;"> for each of the cell oftwo way table is given as:Type of ticketType of flightDomesticInternationalRow totalFirst class2922Business class99125224Economy class514131645Column total278920The expected frequency for each of the cell is obtained using the formula: and the value for each cell is obtained as:Type of ticketType of flightDomesticInternationalRow totalFirst class51Business class156.313067.6870224Economy class450.0978194.9022645Column total642278920The value of the test statistic is obtained as:The value of test statistic is obtained as .The degree of freedom for the test is obtained as:The p-value for the test is obtained as:Note: The p-value for the test is obtained using the MS-excel formula "=CHIDIST( )" and the required probability is obtained as:Decision Rule: If the obtained p-value of the test is less than the level of singificance,we reject the null hypothesis.Otherwise, we fail to reject the null hypothesis.As in the given case, the obtained p-value is less than the level of significance (0.05), We will reject the null hypothesis and conclude that there is sufficient evidence to claim that the type of ticket purchased is not independent of the type of flights.The third option is the correct choice for null and alternative hypotheses as:The type of ticket purchased is independent of the type of flight.The type of ticket purchased is not independent of the type of ticket.The value of the test statistic is 103.605.The p-value for the test is 0.0000.At 0.05 level of significance, we will reject the null hypothesis and conclude that there is sufficient evidence to claim that the type of ticket purchased is not independent of the type of flight.