Discuss the type of situation in which we would want a 95% confidence interval. When would we want a 99% confidence interval?

A 95% confidence interval is typically used when you want to be 95% confident that the true population parameter (like mean, proportion, difference in means, etc.) falls within the interval. This is the most common level of confidence used in many fields of study, including business, psychology, health sciences, and others. It provides a balance between precision (how wide the confidence interval is) and confidence (how sure you are that the true value lies within the interval).

For example, if you are conducting a survey on the average income of households in a city, you might use a 95% confidence interval to estimate this average. This means that you are 95% confident that the true average income falls within your interval.

On the other hand, a 99% confidence interval is used when you want to be 99% confident that the true population parameter falls within the interval. This level of confidence is typically used in situations where the stakes are high and a wrong decision could have serious consequences. However, a 99% confidence interval will be wider than a 95% confidence interval (assuming the same sample data), because to be more confident that you've captured the true parameter, you need to allow for more potential values within the interval.

For instance, if you are conducting a clinical trial for a new drug, you might use a 99% confidence interval to estimate the drug's effectiveness. This is because the consequences of making a wrong decision (like approving a drug that's not effective) are very high. So, you want to be as confident as possible that the true effectiveness falls within your interval.