The housing market recovered slowly from the crisis of 2008. Realtors in one community have recently sampled 36 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss from the peak in 2008 was $9560 with a standard deviation of $1500. a) What assumptions and conditions must be checked before finding a confidence interval and how would you check them?

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**Understanding the Housing Market Post-2008**

The housing market recovered slowly from the crisis of 2008. Realtors in one community have recently sampled 36 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss from the peak in 2008 was $9,560 with a standard deviation of $1,500.

**Analysis Questions:**

a) What assumptions and conditions must be checked before finding a confidence interval and how would you check them?

**Detailed Explanation:**

To determine the reliability of a confidence interval estimate, several assumptions and conditions must be met:

1. **Random Sampling:** Ensure the sample is randomly selected to avoid bias.

2. **Normality:** Given the sample size (n=36) is relatively small, check if the data distribution is approximately normal. This can be assessed using plots such as a histogram or Q-Q plot. For larger samples, the Central Limit Theorem suggests the distribution of the sample mean will be normal.

3. **Independence:** Each observation should be independent of others. This condition is usually met if the sample size is less than 10% of the population.

By verifying these assumptions, you ensure that the confidence interval calculated using the sample data will be valid and reliable for making inferences about the population average loss in home value.
Transcribed Image Text:**Understanding the Housing Market Post-2008** The housing market recovered slowly from the crisis of 2008. Realtors in one community have recently sampled 36 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss from the peak in 2008 was $9,560 with a standard deviation of $1,500. **Analysis Questions:** a) What assumptions and conditions must be checked before finding a confidence interval and how would you check them? **Detailed Explanation:** To determine the reliability of a confidence interval estimate, several assumptions and conditions must be met: 1. **Random Sampling:** Ensure the sample is randomly selected to avoid bias. 2. **Normality:** Given the sample size (n=36) is relatively small, check if the data distribution is approximately normal. This can be assessed using plots such as a histogram or Q-Q plot. For larger samples, the Central Limit Theorem suggests the distribution of the sample mean will be normal. 3. **Independence:** Each observation should be independent of others. This condition is usually met if the sample size is less than 10% of the population. By verifying these assumptions, you ensure that the confidence interval calculated using the sample data will be valid and reliable for making inferences about the population average loss in home value.
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