Emily L.
asked • 12/12/22Confidence Interval
Listed below are the arrival delays (in minutes) of randomly selected United Airlines flights from JFK to SFO. Negative numbers mean that flights arrived that many minutes early based on their scheduled arrival times. Use an 85%, 92%, and 98%, confidence intervals to analyze the on-time performance of this airlines. -10, -32, -13, -9, 49, -18, -30, 14, 18, -12, 11, 3, -7
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1 Expert Answer
Inactive Tutor answered • 06/24/26
Tutor
New to Wyzant
Calc: L1(1) = -10, L1(2) = -32, ... , L1(13) = -7
TInterval(List: L1, Freq: 1, C-Level: 0.85) ≈ {-12.1, 6.562} minutes
TInterval(List: L1, Freq: 1, C-Level: 0.92) ≈ {-14.37, 8.833} minutes
TInterval(List: L1, Freq: 1, C-Level: 0.98) ≈ {-19.04, 13.497} minutes
Because each interval contains 0, it's possible for a flight to arrive on time on this airline. That's the only conclusion I can come up with based on these intervals, as for each of them, it's still possible for a flight to arrive a few minutes earlier or later than expected.
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Inactive Tutor
Our first step is to understand what a confidence interval is. As with all data, you will find a range of values, and we want to get a measure of what you can expect. You can get a single value with a mean, but it doesn't capture the variability in life. A confidence interval strives to get a more realistic measurement by giving us a range that we can reasonably expect to capture the majority of occurrences. For the example in the question, we want to know how early or late we can expect the flights to be, on average. We're calculating this from a sample of 13 flights' arrival times. In reality, this airline might have a hundred thousand flights a year, which is just simply too much for us to calculate, so we use these 13 flights as an approximation, understanding that the 13 flights average is not the true average of timeliness for this airline. If you picked a different random sample of 13 flights from this airline, you would get a different average. An 85% confidence interval would give you a range so that if you conducted about 100 random samples, 85 of the confidence intervals you calculate would contain the true average. It's a confusing concept! But basically your confidence interval is talking about the probability that you caught the true average. The higher the percentage, the wider the interval, and the more likely the real value is included. The formula for your confidence interval is as follows: CI= (sample mean) plus or minus z * (standard deviation)/sqrt(sample size) z is the z score, which you would look up in a z table based on your confidence interval01/07/23