You have a 5% probability of being wrong with a 95% confidence interval. You have a 10% probability of being mistaken with a 90% confidence interval. A 99 percent confidence interval, for example, would be bigger than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent). It is common practice to report both the length of the confidence interval and the associated probability. For example, a 90 percent confidence interval means that there is only a 10 percent chance that the true population mean is actually different from the estimate.

- Is a confidence level of 90 acceptable?
- What is the primary purpose of the 99 confidence interval for a mean?
- What is the level of significance for a 90-confidence interval?
- What is the most accurate confidence interval?
- Why is a 95 confidence interval wider than a 90?
- What does a 95% confidence level mean?
- What does the 99% confidence level in the previous problem tell us?
- What is a good confidence level in statistics?

A 99 percent confidence interval approach is more likely than **a 95 percent confidence interval procedure** to provide intervals that contain the population parameter. A confidence range of 20% to 40% indicates that the population proportion is between 20% and 40%. A confidence interval can be constructed using the percentile method or the normal approximation method. There are many ways to construct a confidence interval, but they all involve calculating two numbers: **(1) a point estimate** of the population parameter and (2) a measure of uncertainty called a standard error.

The goal when constructing a confidence interval is to include the true value of the parameter with **enough certainty** so that we may report that we do indeed have an accurate estimate of it. In order to do this, we need to make sure that our confidence interval contains the true value of the parameter almost every time. We can only do this by making sure that the probability of the confidence interval not containing the true value is very small. This is where the concept of confidence intervals comes in. A confidence interval provides information about how certain we are about the parameter value. If the standard error is small, then we can say with high confidence that the true population parameter lies within the interval.

In statistics, a confidence interval is a range of values for which we can be confident that the true value of the parameter lies within that range. There are two types of confidence intervals: one-sided and two-sided.

The statistical word for how ready you are to be mistaken is "level of significance." With a 95 percent confidence interval, you have **a 5% chance** of being incorrect. With **a 90% confidence interval**, you have **a 10% chance** of being mistaken. These chances will not change regardless of how many people take the test or what their scores were before they took it.

Confidence intervals show how close your estimate is to the true value. They do this by telling you what percentage of observations from the sample would have to agree with your estimate for there to be a 10%, 20%, 30%, etc., chance that you have made a mistake. For example, if I ask you to guess my age, then tell you that 95 out of 100 people over 40 feel like I do, we would say that I can be as old as I want to be since there is only a 5% chance that I am wrong. If I tell you that 99 out of 100 people over 40 feel like I do, we would say that I can be as old as I want to be since there is only a 1% chance that I am wrong.

Confidence intervals work best with large samples. There must be at least 15 people in your sample for the 90% confidence interval to make any sense. Trying to calculate a confidence interval for a sample size of 7 is almost impossible because there won't be enough data to be confident about the result.

The 99 percent confidence interval is more precise than the 95 percent confidence interval. Therefore, the 99 percent confidence interval is the most accurate interval for estimating the true population mean.

A 99 percent confidence interval, for example, will be broader than a 95 percent confidence interval because we need to include more alternative values within the interval to be more certain that the genuine population value falls within the interval. The most often used confidence level is 95%. Therefore, a 95% confidence interval will be wider than **a 90% confidence interval**.

A 95 percent confidence interval is a set of data that contains the real mean of the population 95 percent of the time. This is not the same as a range containing 95% of the data. There are different ways to interpret this statistic, but they all assume that the data being analyzed come from a normal distribution.

It is important to remember that confidence intervals provide information about **the true value** of the parameter being estimated. They do not estimate the parameter directly; instead, they show you what the parameter would have to be in order for your conclusion to be correct 95% of the time. For example, if I were to ask you to guess my age, most people would say around 30. If I asked you to tell me exactly how old I was 95% of the time, you would need to look up **the exact figure** for me. That number is 63 and it comes from applying the formula:

Where n is the number of samples (in this case, 95) and s is the standard deviation of the sample (which in this case is 33).

This means that if you repeated the test on **a new sample** of size n = 95 and s = 33 then the true age would have to be within one standard deviation of **the new sample** mean 25% of the time for there to be a 5% chance of getting it wrong.

A set of possible responses There is a 99.9% likelihood that this interval contains the population proportion. The interval will include 99.9% of all sample proportions. The population percentage will be contained in 99 percent of the confidence intervals with **this margin** of error.

Confidence ratings of 90, 95, and 99 percent are widely employed in surveys. If the confidence level is set at 95%, a derived statistical value based on a sample would likewise be true for the entire population within the stated confidence level, with **a 95% chance**. Setting the confidence level at 99% ensures that the result is accurate to within 1 percentage point.

Confidence levels are important factors in survey research. A researcher may want to use a high confidence level to establish rigorous criteria for including or excluding participants from a study. For example, if the goal is to learn about how Americans view President Obama's handling of health care policy, a researcher might want to know with 99% certainty that results obtained from a sample of 1,000 people are accurate to within 3 percentage points. In this case, it would not make sense to ask anyone under the age of 18 because they cannot give informed consent and also be unbiased observers. Similarly, if one wants to know whether young adults aged 18-24 are more likely than others to vote in elections, it makes no sense to ask older people because they probably voted in earlier elections that we do not have data for.

There are two main types of errors when using statistics: **random error** and systematic error. Random error occurs when someone takes an action that affects the outcome of **a statistical test**, but does so by chance alone.