Contents

- 1 What does a negative to positive confidence interval mean?
- 2 What does a positive confidence interval mean?
- 3 Can a confidence interval include zero?
- 4 What happens when confidence interval contains zero?
- 5 How is the confidence interval and the confidence level related?
- 6 What is the 95% confidence interval for the census?

## What does a negative to positive confidence interval mean?

The confidence interval (whatever it is) will by definition fall more in the negative side than the positive side. However, if you reversed the calculation and did treatment-control instead, you would get a range falling more in the positive side. It would not affect your final conclusion.

## What does a positive confidence interval mean?

The men have higher mean values on each of the other characteristics considered (indicated by the positive confidence intervals). The confidence interval for the difference in means provides an estimate of the absolute difference in means of the outcome variable of interest between the comparison groups.

**What happens when confidence interval is negative?**

If the lower endpoint of a confidence interval for a population percentage is negative, it is completely legitimate to replace the lower endpoint by zero: It does not decrease the confidence level. Similarly, a population percentage cannot be greater than 100%.

**Can a confidence interval have a negative value?**

If the t value is negative, then the confidence intervals will also contain negative numbers. So long as the confidence interval does not cross zero (does not contain one positive and one negative number), it will be much easier to interpret it if you use the absolute value of the confidence interval.

### Can a confidence interval include zero?

If the confidence interval (with your chosen level of confidence) includes 0, that implies you think 0 is a reasonable possibility for the true value of the difference. In general, by ‘significant’ people usually mean that they no longer believe the null hypothesis (0) is a reasonable possibility.

### What happens when confidence interval contains zero?

If your confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.

**What confidence interval is acceptable?**

Sample Size and Variability The level of confidence also affects the interval width. If you want a higher level of confidence, that interval will not be as tight. A tight interval at 95% or higher confidence is ideal.

**Can a confidence interval of a positive value be negative?**

Defining a confidence interval as mean +/- sample standard deviation implicitly assumes a normal, or at least symmetric, distribution. If we choose a distribution that itself is non-negative, say χ 2 or Poisson, then the confidence interval will never go below zero. It will, however, be asymmetric.

The length of the confidence interval and the confidence level measure how accurately we are able to estimate the parameter from a sample. If a short interval has high confidence, the data allow us to estimate the parameter accurately.

## What is the 95% confidence interval for the census?

We can increase the expression of confidence in our estimate by widening the confidence interval. For the same estimate of the number of poor people in 1996, the 95% confidence interval is wider — “35,363,606 to 37,485,612.” The Census Bureau routinely employs 90% confidence intervals.

**What is the probability that the interval covers the parameter?**

(One could say that after collecting the data, the chance that the interval covers the parameter is either 0 or 100%.) Typically, we never learn whether the interval covers the parameter, but our ignorance is not a probability (at least, not according to the frequency theory of probability used in this book).