TAKWIMU

Kikokotoo cha nafasi ya uhakika

Kokotoa nafasi ya uhakika kwa wastani au asilimia ya sampuli. Weka data ya muhtasari, chagua kiwango cha uhakika, na uone masafa, ukingo wa kosa na makadirio.

Percentage interval

Interval result

95%

Lower bound

41.179%

Sample estimate

48%

Upper bound

54.896%

Interval line

41.179%48%54.896%

Margin of error

+/- 6.859%

Standard error

3.533%

Critical value

1.96

Method: Wilson interval for a percentage

This estimates a population percentage from counted successes and total trials.

The confidence level describes how often this method would capture the true value across repeated samples.

Saved on this device

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Understanding confidence intervals

What the interval means

A confidence interval gives a likely range for a population average or percentage based on your sample. A 95% confidence level means that, across repeated random samples, this method would include the true value about 95 times out of 100.

Average or percentage

Use Average for measured values such as time, height, score, or cost. Use Percentage for yes/no counts such as 96 yes answers out of 200 responses.

Formula choices

Average mode uses a t interval because the population standard deviation is usually unknown. Percentage mode uses the Wilson interval because it behaves better than the simple normal interval for small samples and results near 0% or 100%.

Common mistakes

Treating the range as a guarantee

The interval still depends on how the sample was collected. A biased sample gives a biased interval.

Using percentage mode for averages

Do not enter an average score as successes out of total. Use Average mode for measured numbers.

Ignoring tiny sample warnings

Very small samples make the range wider and more assumption-heavy. Collect more data when the decision matters.

Tips and examples

Compare confidence levels

Switch between 90%, 95%, and 99% to see how cautious the interval becomes.

Survey percentage example

96 yes answers out of 200 at 95% confidence gives about 41.2% to 54.9%.

Average example

A sample average of 100 with sample standard deviation 12 and 11 values gives about 91.9 to 108.1 at 95% confidence.

FAQ

What does a 95% confidence interval mean?

It means the method has 95% long-run coverage across repeated samples. It does not promise that one finished interval has a personal 95% chance after the data is fixed.

Why is the percentage interval uneven?

The Wilson method adjusts the center and width of the interval. That can look uneven, but it gives better behavior for small counts and for 0% or 100% sample results.

Can I use this with non-random data?

You can calculate the range, but the result may not describe the real population well. The sample collection method matters as much as the formula.

Is this the same as a prediction interval?

No. This estimates a population average or percentage. It does not predict the range for one future observation.