Final answer:
The events are not independent because there is a higher probability of receiving a mile for every dollar spent among those who charge more than $2,000, compared to the general probability among all respondents.
Step-by-step explanation:
In order to determine if using a credit card that gives a mile of air travel for each dollar spent and charging more than $2,000 per month are independent events, we need to look at the definition of independence in probability.
Independent events occur if the probability of one event occurring does not affect the probability of the other event occurring. Based on the information provided, 30% of respondents charge more than $2,000 per month. Of those, 80% use a credit card that provides air miles. If we compare this to the fact that 35% of all respondents use a credit card that gives them a mile of air travel for every dollar they charge, we can see a discrepancy.
To be independent, the probability of respondents charging more than $2,000 should be the same irrespective of whether they receive miles for every dollar charged. However, 80% (which is more than the overall 35%) of those who spend more than $2,000 do get air miles. This indicates a dependence between the two events because those who spend more are more likely to have a card with this reward.