The real estate industry claims that it is the best and most effective system to market residential real estate. A survey of randomly selected home sellers in Illinois found that a 95% confidence interval for the proportion of homes that are sold by a real estate agent is 69% to 81%. Four interpretations are offered below. Three are incorrect and one is correct. Find the three incorrect interpretations and explain the error in each of them.
1. We are 95% confident, based on this sample, that between 69% and 81% of all homes in Illinois are sold by a real estate agent.
2. We are 95% confident that between 69% and 81% of homes in this survey are sold by a real estate agent.
3. 95% of all homes in Illinois are sold by a real estate agent.
4. 95% of all random samples of home sellers in Illinois will show that between 69% and 81% of homes are sold by a real estate agent.
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