Final answer:
To estimate a confidence interval for average home value loss, one must check for random sampling, normality of the population distribution, independence of observations, and a sufficient sample size. These ensure the sample is representative and the confidence interval calculations are valid.
Step-by-step explanation:
Before estimating a confidence interval for the average loss in home value, certain assumptions and conditions must be checked to ensure the validity of the results. These include:
- Random sampling of homes to ensure that the sample is representative of the population.
- The normality of the population distribution, especially important when the sample size is small. If the sample size is large, the Central Limit Theorem suggests that the sampling distribution of the mean is approximately normal.
- Independence of sample observations, which means the value of one observation does not influence or predict another. This is often assured if the sample size is less than 10% of the population.
- A sufficient sample size, which is generally considered large if n > 30 for approximate normality. For smaller samples, the data should be nearly normally distributed without outliers.
To construct a confidence interval, the level of confidence, whether the standard deviation of the population is known, the sample size, and whether the sample is normally distributed must be taken into account. With these conditions met, you can calculate the confidence interval to estimate the population mean with a desired level of assurance, expressed as a percentage (e.g., 90%, 95%).