Question

You construct two confidence intervals to estimate the mean number of passengers on all air routes. For which sample below would you expect a smaller margin of error (PLEASE CIRCLE the appropriate letter and then briefly EXPLAIN)

1) A random sample of 50 air routes between Seattle, WA and Portland, OR

2) A random sample of 50 air routes starting and ending in many different cities across the USA

Answer 1

Margin of error depends on sample size (which are equal in both cases), z or t values (which are equal again because we will find margin of error on same confidence level) and sample or population standard deviation (this is the part which will change)

Standard deviation is a measure about how much spread is there in data about the mean. Larger standard deviation lead higher margin of error and smaller standard deviation lead to smaller margin of error.

In case 2) we are taking 50 air routes which may be larger than the case 1) routes or shorter than case 1) because it is considering 50 air routes which are ending in many different cities across the USA. So, there will be great variability comparison to case 1) 50 air routes because those are between 2 cities hence there will be variation but not that much.

So, I expect a smaller margin of error in case 1) A random sample of 50 air routes between Seattle, WA and Portland, OR.

Please comment if any doubt. Thank you.