McJilton Airlines’ public relations department says that the airline rarely loses passengers’ luggage. It also claims...

McJilton Airlines’ public relations department says that the airline rarely loses passengers’ luggage. It also claims that when it does lose luggage, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed travelers with lost luggage found that 103 out of 122 people had their luggage returned to them within 24 hours. Can the consumer group dispute the claim, with 95% confidence?

Expert Solution

One-Proportion Z test

The following information is provided: The sample size is N = 122, the number of favorable cases is X = 103 and the sample proportion is pˉ=X/N=103/122=0.8443, and the significance level is α=0.05

(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho: p =0.9
Ha: p <0.9 (Dispute the claim would mean that the proportion is less than 90%)
This corresponds to a Left-tailed test, for which a z-test for one population proportion needs to be used.

(2a) Critical Value
Based on the information provided, the significance level is α=0.05, therefore the critical value for this Left-tailed test is Zc=-1.6449. This can be found by either using excel or the Z distribution table.

(2b) Rejection Region
The rejection region for this Left-tailed test is Z<-1.6449

(3) Test Statistics
The z-statistic is computed as follows:

(4) The p-value
The p-value is the probability of obtaining sample results as extreme or more extreme than the sample results obtained, under the assumption that the null hypothesis is true. In this case,
the p-value is p =P(Z<-2.0521)=0.0201

(5) The Decision about the null hypothesis
(a) Using traditional method
Since it is observed that Z=-2.0521 < Zc=-1.6449, it is then concluded that the null hypothesis is rejected.

(b) Using p-value method
Using the P-value approach: The p-value is p=0.0201, and since p=0.0201≤0.05, it is concluded that the null hypothesis is rejected.

(6) Conclusion
It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is less than 0.9, at the 0.05 significance level.

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orchestra answered 2 years ago

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