Housing prices in the U S in 2021 had the largest jump in 30 years Recently in one large community real estate agents randomly sampled 31 bids from potential buyers to estimate the average gain in home value The sample showed the average gain was 9480 with a standard deviation of 1038 Complete parts a through c a What assumptions and conditions must be checked before finding a confidence interval How would one check them OA The data are assumed to be independent and from a Normal population Check the independence assumption with the Randomization Condition Check the Normal population assumption with the Nearly Normal Condition using a histogram OB The data are assumed to be independent and to have a sample size that is large enough to have a sampling distribution that is approximately Normal Check the independence assumption with the Randomization Condition Check the sample size assumption by ensuring that there are at least 10 successes and 10 failures OC The data are assumed to be dependent and to have a sample size that is large enough to have a sampling distribution that is approximately Normal Check the independence assumption by ensuring that there are at least 10 successes and 10 failures O D The data are assumed to be independent and from a Normal population Check the independence assumption with the Nearly Normal Condition using a histogram Check the Normal population assumption with the Randomization Condition b Find a 90 confidence interval for the mean gain in value per home Round to the nearest dollar as needed c Interpret this interval and explain what 90 confidence means in context Choose the correct answer below OA It can be said with 90 confidence that the gain in value for a randomly selected home in this community is within this interval OB It can be said with 90 confidence that the mean gain in value per home in this community is within this interval OC This interval contains the true m an gain in value per home in this community 95 of the time O D 90 of homes in this community have a gain in value within this interval