In 2020, 16.9% flights arriving to LAX were 15 minutes or more late. Theaverage “arriving late” time was 11.93 minutes per flight. Investigators want tosee whether the delay times have changed since 2020.The available data set from 2021 shows 10 randomly selected airlines and theirarrival information for each month.SHOW YOUR WORK FOR EACH QUESTION!1. First you need to investigate whether the proportion of late flights has changed from 16.9%.a. Write the null and alternative hypotheses.b. Check the condition(s) for the appropriate hypothesis test
Question
In 2020, 16.9% flights arriving to LAX were 15 minutes or more late. Theaverage “arriving late” time was 11.93 minutes per flight. Investigators want tosee whether the delay times have changed since 2020.The available data set from 2021 shows 10 randomly selected airlines and theirarrival information for each month.SHOW YOUR WORK FOR EACH QUESTION!1. First you need to investigate whether the proportion of late flights has changed from 16.9%.a. Write the null and alternative hypotheses.b. Check the condition(s) for the appropriate hypothesis test
Solution
a. Null and Alternative Hypotheses:
Null Hypothesis (H0): The proportion of late flights in 2021 is the same as in 2020, i.e., p = 0.169.
Alternative Hypothesis (H1): The proportion of late flights in 2021 is different from that in 2020, i.e., p ≠ 0.169.
b. Conditions for the appropriate hypothesis test:
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Randomness: The data should be collected randomly. In this case, the data is from 10 randomly selected airlines, so this condition is met.
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Normality: The sample size should be large enough such that the sampling distribution of the proportion is approximately normal. This is often assessed using the rule of thumb that np and n(1-p) should both be greater than or equal to 10. Without knowing the total number of flights (n), we can't check this condition here.
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Independence: The sample observations should be independent. In this case, the lateness of one flight should not affect the lateness of another, so this condition is likely met.
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