The sample of house sales we looked at in Exercise 31 also...

The sample of house sales we looked at in Exercise 31 also listed whether homes were new construction or not. Find and interpret a 95$\%$ confidence interval for how much more an agent can expect to sell a new home for. (From technology, df = $197.8 .$ ) Here are the summaries and box plots of the Sale Prices:

Key Concepts

Degrees of Freedom

Degrees of freedom refer to the number of independent values in a calculation that are free to vary. In the context of estimating a confidence interval using the t distribution, degrees of freedom typically depend on the sample size and are used to determine the appropriate critical value for constructing the interval.

Confidence Interval

A confidence interval is a range of values calculated from sample data that is likely to contain the true value of an unknown population parameter. It provides an estimated range believed to be the true difference or effect size based on the reliability or precision of the sample data, accompanied by a confidence level such as 95% which indicates how often this interval would include the true parameter if repeated samples were taken.

Interpretation of Confidence Interval

Interpreting a confidence interval involves understanding that if the process used to generate the interval is repeated numerous times, a specified percentage (e.g., 95%) of these intervals would contain the true population parameter. It is a statement about the method's reliability rather than a probability statement about the parameter itself.

t Distribution

The t distribution is a probability distribution used in situations where the sample size is small or the population standard deviation is unknown. It is similar to the normal distribution but has heavier tails, which allows for the increased uncertainty inherent in estimating the standard deviation from a small sample.

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