In an article published last year, the Federal Transportation Department claimed

Question

In an article published last year, the Federal Transportation Department claimed that Southwest Airlines suffers from a 7% rate of no-shows. That is, the article claimed that 7% of the people who make reservations for Southwest Airlines flights don’t show-up. Whether this is the result of forgetfulness, not getting to the airport on-time, or one of many other reasons is not known, but empty seats on their flights is something Southwest Airlines wants to minimize. Six months ago, a new procedure was instituted whereby reservations on Southwest Airlines flights are confirmed via a text, an email, and a voice mail on the day preceding the actual flight. A study is then made of 5218 randomly selected reservations made under the new system. If 338 no-shows are recorded, does the new system seem to have resulted in a lower no-show rate than the one published in last year’s Federal Transportation report?

(a) What are the null and alternative hypotheses? Use the appropriate symbols to write each. (b) Which of the different types of mathematical models probability distributions (the Binomial Distribution, Normal Distribution, T Distribution) will you use to compute the P-Value? In your detailed explanation include a context-specific check of all the requisite conditions that must be satisfied before you can use the specific model you chose (c Compute the P-value, report your answer with at least five digits after the decimal point. Specify the name of the TI-84 function you use, include the values you input into this calculator function. (d) If you decide to perform this hypothesis test at the 5% level of significance, what do you conclude? Please write your conclusion in plain English about whether-or-not your hypothesis test's results lead you to conclude that the new confirmation system results in a lower no-show rate than the one published in last year's Federal Transportation report. (e) If, in reality, the new confirmation system results in a lower no-show rate than the one published in last year's Federal Transportation report, have you made a Type I or Type II error in part (d)? Explain. If you have made an error, tell which kind of error (Type I or Type you made.

Explanation / Answer

Solution:

Sample proportion:: p-hat = 338/5218 = 0.065
a) a symbolic statement of the null and alternative hypotheses,
Ho: p >= 0.07
Ha: p < 0.07

b) A symbolic statement comprised of the correct mathematical symbols depicting the specific probability of an event that the P-value represents
z(0.065) = (0.065-0.07)/sqrt[0.07*0.93/5218] = -1.416
p-value = P(z < -1.416) = 0.078

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