# Developing Hypothesis and Understanding Possible Conclusions for Proportions

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## Question

An airline company claims in a recent advertisement that more than 94% of passenger luggage that it lost is recovered and reunited with the customer within 1 day. Hunter is a graduate student studying statistics. For a research project, Hunter wants to find out whether there is convincing evidence in support of the airline company's claim. He randomly selects 315 passengers of the airline whose luggage was lost by the airline and found that 276 of those passengers were reunited with their luggage within 1 day. Are all of the conditions for this hypothesis test met, and if so, what are the null and alternative hypotheses for this hypothesis test?

All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.94Ha:p<0>

All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:p=0.94Ha:p>0.94.

First verify whether all of the conditions have been met. Let p be the population proportion for the airline passengers whose luggage was lost by the airline and were reunited with their luggage within 1 day.

1. Since Hunter is completing a survey where there are two independent outcomes, the proportion follows a binomial model.
2. The question states that Hunter randomly selected the airline passengers whose luggage was lost by the airline.
3. The expected number of successes, np=296.1, and the expected number of failures, nq=n(1−p)=18.9, are both greater than or equal to 5.

Since all of the conditions for this hypothesis test have been satisfied, determine the null and alternative hypotheses. Since Hunter is determining whether the proportion for reuniting passengers with their luggage within 1 day is greater than 94%, the null hypothesis is that p is equal to 0.94 and the alternative hypothesis is that p is greater than 0.94. The null and alternative hypotheses are shown below.

{H0:p=0.94Ha:p>0.94