Airline Baggage Controversy: Are Airlines Really Losing Our Bags?

Are Airlines Really Losing Flier's Baggage?

Based on the data provided, is there sufficient evidence to support the airline spokesman's claim that fewer than 1% of all bags fail to arrive at their destinations with the passengers?

Analysis and Conclusion

Based on a hypothesis test for a proportion, and considering a 5% level of significance, there is not enough evidence to refute the airline's claim that less than 1% of bags fail to arrive at their destinations with the passengers. The calculated P-value is greater than the significant level, and the calculated test statistic is not in the Rejection Region.

In the past six months, there have been numerous complaints about airlines losing passengers' baggage. However, airline representatives have stated that the issue is much smaller than what has been portrayed in newspaper articles. One airline spokesman boldly claimed that fewer than 1% of all bags fail to reach their destinations with the passengers.

To validate this claim, a study was conducted where 800 bags were selected at various airports in the United States and checked with this specific airline. Out of the 800 bags, only 6 failed to reach their destinations upon arrival of their owners.

By performing a hypothesis test for a proportion with a 5% level of significance, it was determined that there is insufficient evidence to contradict the airline's assertion. The calculated P-value was greater than the specified significance level, and the test statistic did not fall into the Rejection Region.

This outcome indicates that the airline's statement of less than 1% of bags failing to arrive at their destinations is statistically supported by the data collected. The Rejection Region, which contains values that would lead to rejecting the null hypothesis, was not encountered in this analysis.

Understanding hypothesis testing for proportions is essential in evaluating claims and drawing conclusions based on statistical significance. In this scenario, the results suggest that the airline's assertion regarding baggage delivery accuracy is reliable and not to be refuted.