Question

An airline employee wants to estimate the proportion of the airline's flights that were on time in 2021 (where a flight is considered "on time" if it arrives no later than 15 minutes after the advertised arrival time). A survey from 2020 indicates that year 84% of their flights were on time. Using this prior estimate as a starting point how many flights from 2021 need to be sampled randomly to estimated the proportion of the airline on time flights to within 3% with 90% confindence?

Answer 1

To estimate the proportion of on-time flights in 2021 within a 3% margin of error and 90% confidence, at least 722 flights need to be sampled randomly.

Step-by-step explanation:

To estimate the proportion of on-time flights in 2021, we can use the formula:

n = (Z^2 * p * (1-p)) / E^2

where:

• n is the required sample size
• Z is the Z-score corresponding to the desired confidence level (in this case, Z = 1.645 for 90% confidence)
• p is the prior estimate of the proportion of on-time flights (0.84)
• E is the desired margin of error (0.03)

Plugging in these values, we can calculate the sample size:

n = (1.645^2 * 0.84 * (1-0.84)) / 0.03^2 = 721.6

Since we cannot have a fractional sample size, we need to round up to the nearest whole number. Therefore, we need to randomly sample at least 722 flights from 2021.