90 Confidence Interval Calculator Given X and N

This calculator computes the 90% confidence interval for a proportion given x successes and n trials. The confidence interval provides a range of values that is likely to contain the true population proportion with 90% confidence.

What is a 90% Confidence Interval?

A 90% confidence interval is a range of values that is likely to contain the true population proportion with 90% confidence. It's calculated based on sample data and provides a measure of the uncertainty associated with the estimate.

For example, if you survey 100 people and find that 60% support a particular policy, the 90% confidence interval might be between 52% and 68%. This means you can be 90% confident that the true proportion of people who support the policy is between 52% and 68%.

How to Use This Calculator

Enter the number of successes (x) in your sample.
Enter the total number of trials (n) in your sample.
Click "Calculate" to compute the 90% confidence interval.
Review the results and interpretation.

The Formula

The formula for the 90% confidence interval for a proportion is:

p̂ ± z*(√(p̂*(1-p̂)/n))

Where:

p̂ is the sample proportion (x/n)
z is the z-score for 90% confidence (approximately 1.645)
n is the sample size

This formula calculates the lower and upper bounds of the confidence interval.

Worked Example

Suppose you conducted a survey of 100 people and found that 60 supported a new policy. Let's calculate the 90% confidence interval:

Example Calculation

Given:

Number of successes (x) = 60
Number of trials (n) = 100

Sample proportion (p̂) = 60/100 = 0.60

Standard error = √(0.60 * 0.40 / 100) ≈ 0.049

Margin of error = 1.645 * 0.049 ≈ 0.081

90% Confidence Interval = 0.60 ± 0.081 → (0.519, 0.681) or 51.9% to 68.1%

Interpreting Results

The confidence interval provides a range of values that is likely to contain the true population proportion. For the example above, we can be 90% confident that the true proportion of people who support the policy is between 51.9% and 68.1%.

If the confidence interval is wide, it indicates more uncertainty in the estimate. A narrower interval suggests a more precise estimate.

FAQ

What does a 90% confidence interval mean?: It means that if you were to take many samples and calculate a 90% confidence interval for each, about 90% of those intervals would contain the true population proportion.
How does sample size affect the confidence interval?: A larger sample size generally results in a narrower confidence interval, providing a more precise estimate of the population proportion.
Can I use this calculator for other confidence levels?: This calculator specifically calculates the 90% confidence interval. For other confidence levels, you would need to adjust the z-score accordingly.
What if my sample proportion is 0% or 100%?: The formula for the confidence interval assumes that the sample proportion is between 0% and 100%. If your sample proportion is exactly 0% or 100%, the confidence interval will be undefined.
How do I know if my sample is representative?: A representative sample should be randomly selected and large enough to accurately reflect the population. Consider factors like sample size, sampling method, and potential biases when assessing representativeness.