An airline has surveyed a simple random sample of air travellers to find out whether they would be interested in paying a higher fare in order to have access to e-mail during their flight. Of the 400 travellers surveyed, 80 said email access would be worth a slight extra cost.

Determine the sample proportion of air travellers who are in favour of the airline’s email idea

Question

An airline has surveyed a simple random sample of air travellers to find out whether they would be interested in paying a higher fare in order to have access to e-mail during their flight. Of the 400 travellers surveyed, 80 said email access would be worth a slight extra cost.

Determine the sample  proportion of air travellers who are in favour of the airline’s email idea

BlackTom AI · Accepted Answer

We start by clearly restating the scenario and what is being asked.
The question asks for the sample proportion of air travellers who are in favour of the airline’s email idea, given that 80 out of 400 travellers surveyed said email access would be worth a slight extra cost.
Next, recall the definition: the sample proportion, often denoted p̂, is computed as the number in favor divided by the total number surveyed, i.e., p̂ = x/n.
Here, x represents the count in favor (80 travellers) and n represents the total sample size (400 travellers).
Compute the ratio: p̂ = 80 / 400.
Simplify the fraction by dividing numerator and denominator by 80: p̂ = 1 / 5 = 0.20.
As a decimal, this is 0.20, which can also be expressed as 20%. 
Now, note the structure of the data: we have a simple random sample of 400 travellers, with 80 in support, so the estimate is based on this observed proportion rather than any broader population parameter.
Since the prompt did not provide explicit answer choices to evaluate, focus on the calculation steps: you divide the favorable count by the total sample size, which yields 0.20. This follows directly from the definition of a sample proportion and the given counts.
In summary, the sample proportion of travellers in favour is 0.20 (or 20%), because 80 of 400 travellers expressed interest in paying a higher fare for email access.

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