Will your flight get you to your destination on time? To the right are a histogr

Question

Will your flight get you to your destination on time? To the right are a histogram and summary statistics for the percentage of delayed arrivals each month from 2001 to 2006. Consider these data to be a representative sample of all months. There is no evidence of a time trend. (The correlation of Flights Delayed % with time is r= 0.013.

N=72

Y bar = 24.6250

s= 3.19270

1) Check the assumptions and conditions for inference about the mean. Select all that apply.

All of the assumptions and conditions for inference about the mean are met.

The randomization condition is not met and the sample is not suitably representative.

The 10% condition is not met.

The nearly normal condition is not met.

The independence assumption is not met.

2) Find a 99% confidence interval for the true percentage of flights that arrive late.

_____ < u (delayed flight) < ______

3) Interpret this interval for a traveler planning to fly. Choose the correct answer below

A randomly selected month has a 99% chance of having a delayed flight percentage within the interval.

99% of all months have delayed flights rates within the interval.

There is a 99% chance that the true mean monthly percentage of delayed flights is within the interval.

We can be 99% confident that the interval contains the true mean monthly percentage of delayed flights.

Explanation / Answer

1. The delayed arriavls for each month from 2001 to 2006 are recoreded. The data do come from randomized survey, thus delayed arrivals are not likely to be independent. Thus, randomization condition is met.

10% condition: 72 delayed arrivals is far less than 10% of all delayed arrivals. Thus, 10% condition is met.

Nearly normal condition: [note histogram is not dispalyed] If histogram is symmetric and unimodal, then nearly normal condition is supposed to ffollowed.

Independence assumption: for one sample test for mean, independence assumption for groups is not required to be checked.

2. For normal population, and unknown population standard deviation, use one-sample t test for population mean percentage of delayed flights, mu=ybar+-talpha/2, df=n-1 (s/sqrt n), where, ybar is sample mean, t is t critical at alpha/2 (alpha=0.01, alpha/2=0.005), and n-1 degrees of freedom, s is ample standard deviation, and n is sample size.

=24.6250+-2.647(3.1927/sqrt 72)

=(23.629, 25.621)

By definition of confidence interval the first three options are naturally rejected. One can be 99% confident that the interval contains the true mean monthly percentage of delayed flights.

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