Please help me explain. i believe the gold package would be best because it give the least margin of error for the most sample listings. Please help me with my confidence statement

35511 has hired your company to analyze the Northeast home 11stmg pr1ces in order to give information to their agents about the mean listing price at 95% condence. Your company offers three analysis packages: one based on a sample size of 100 listings= one based on 1,000 listings, and another based on a sample size of 4,000 listings. Because there is an additional cost for data collection, your company charges more for the package with 4,000 listings than for the package with 100 listings. Bronze Package Sample size of 100 listings: 95% condence interval for the mean of the Northeast house listing price has a margin of error of $24,500 Cost for service to BECK: $2,000 Silver Package Sample size of 1,000 listings: 95% condence interval for the mean of the Northeast house listing price has a margin of error of $1150 Cost for service to BECK: $10,000 Gold Package Sample size of 4,000 listings: 95% condence interval for the mean of the Northeast house listing price has a margin of error of $3,900 Cost for service to BECK: $25,000 The BEER management team does not understand the tradeoff between condence level, sample size, and margin of error. 1335K would like you to come back with your recommendation of the sample size that would proyide the sales agents with the best understanding of northeast home prices at the lowest cost for service to 1335K. In other words, which option is preferable? Spending more on data collection and having a smaller margin of error Spending less on data collection and having a larger margin of error Choosing an option somewhere in the middle Formulate a recommendation and write a condence statement in the context of this scenario. For the purposes of writing your condence statement, assume the sample mean house listing price is $310,000 for all packages. "I am [it] % condent the true mean . . . [in context].\" Explain the factors that went into your recommendation, including a discussion of the margin of error