What is the confidence interval and interpretation of the interval for that tier?

A confidence interval is a range of estimates for a population parameter using sample statistics. On the other hand, the margin of error is a statistic which describes how the estimate may differ from the real population value. ​In this equation, CI refers to confidence interval, is the sample mean (estimate), z is the confidence level value, s is the standard deviation, and n is the sample size. The value is the margin of error. As seen from the formula, the margin of error is affected by the sample size and confidence level. It would increase with the confidence level, but it would decrease with the square root of the sample size.
​In the case of the Northeast home listing prices, increasing the sample size involves spending more effort, money and time for data collection. This is the reason why Gold Package (4,000 listings/\$25,000) is more expensive than Silver (1,000 listings/\$10,000) and Bronze (100 listings/\$2,000) Package. However, increasing the sample size would also shrink the margin of error. Smaller margin of error would produce a more accurate estimate of the population parameter, which is the mean home listing prices in the Northeast Region.
​When estimating a population parameter, it is better to acquire a more accurate data. In this case, getting an accurate data would require large sample size. However, as seen from package list, the Gold Package is expensive (\$25,000). On the other hand, using small sample size would produce a large margin of error. In addition, 100 listings may not accurately represent the population of house listings. It should also be considered that there are thousands of active house listing in a single state. The best option would be somewhere in the middle, which is the Silver Package. It uses, 1,000 listings (10 times large than Bronze and only 4 times smaller than Gold). The package also produces a margin of error of \$7,750 (almost twice of the Gold and more than thrice of the Bronze).
Hi Jonathan:
Good start. Can you explain this statement “z is the confidence level value”? It’s really unclear as z is a z-score that we find using the confidence level, but it’s not the actual value of the confidence level. Also, in this example no changes are being made to the confidence level. You mentioned selection of the silver package. What is the confidence interval and interpretation of the interval for that tier?
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