Use Technology to Calculate A 90 Confidence Interval

A 90% confidence interval is a range of values that is likely to contain the true population parameter with 90% probability. This calculator helps you compute confidence intervals using technology, such as statistical software or programming languages.

What is a 90% Confidence Interval?

A 90% confidence interval is a statistical range that suggests there is a 90% probability that the true population parameter lies within this interval. It is commonly used in hypothesis testing and estimation.

Key points about confidence intervals:

The confidence level (90%) represents the probability that the interval contains the true parameter.
The margin of error is the distance from the sample statistic to the ends of the interval.
Confidence intervals are wider for smaller sample sizes and narrower for larger sample sizes.

How to Calculate a 90% Confidence Interval

To calculate a 90% confidence interval, you need the sample mean, sample standard deviation, and sample size. The formula for the confidence interval is:

Confidence Interval = Sample Mean ± (Critical Value × (Standard Deviation / √Sample Size))

The critical value for a 90% confidence interval is approximately 1.645 for a normal distribution.

Note: This calculator assumes a normal distribution. For non-normal data, consider using bootstrapping or other methods.

Example Calculation

Suppose you have a sample of 30 observations with a mean of 50 and a standard deviation of 10. The 90% confidence interval would be calculated as follows:

Lower Bound = 50 - (1.645 × (10 / √30)) ≈ 46.4

Upper Bound = 50 + (1.645 × (10 / √30)) ≈ 53.6

This means we are 90% confident that the true population mean lies between 46.4 and 53.6.

Interpreting the Results

When you calculate a 90% confidence interval, you are stating that if you were to take many samples and compute a confidence interval for each, approximately 90% of those intervals would contain the true population parameter.

Common interpretations:

If the interval includes the hypothesized value, you fail to reject the null hypothesis.
If the interval does not include zero, the effect is statistically significant.
Wider intervals indicate more uncertainty in the estimate.

FAQ

What does a 90% confidence interval mean?

A 90% confidence interval means that if you were to take many samples and compute a confidence interval for each, approximately 90% of those intervals would contain the true population parameter.

How does sample size affect the confidence interval?

Larger sample sizes result in narrower confidence intervals because the estimate of the population parameter is more precise. Smaller sample sizes lead to wider intervals due to increased uncertainty.

Can I use this calculator for non-normal data?

This calculator assumes a normal distribution. For non-normal data, consider using bootstrapping or other methods to compute confidence intervals.

What is the critical value for a 90% confidence interval?

The critical value for a 90% confidence interval is approximately 1.645 for a normal distribution.

How do I report a confidence interval?

Report confidence intervals in the form "lower bound to upper bound" with the confidence level, such as "46.4 to 53.6 (90% CI)."