﻿ ▷ Formula for Confidence Interval - Free - 2021

2 Type of Confidence Intervals

1) Confidence Interval for Mean

Sample 95% Confidence Interval Problem

What is the 95% Confidence Interval of your sample of bowling scores with mean x̄=200 and standard deviation σ=10 and sample size n=100 ?
CI-Setup: x̄ ± z*σ/√(n)
Here, 200 ± 1.96 * 10/√(100)
200 ± 1.96 * 10/10
200 ± 1.96*1
Finally, the 95% Confidence Interval is [198 , 202]
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2) Confidence Interval for Proportion

Sample 95% Proportion Confidence Interval Problem

What is the 95% Proportion Confidence Interval of your sample of students that have seen "Titanic" with x=20 favorable replies and sample size n=30 ?
CI-Setup: p̂ ± z*√(p̂*(1-p̂)/n)
Here, 20/30 ± 1.96 * √((2/3*1/3)/30)
2/3 ± 1.96 * √(2/270)
.6666 ± 1.96 * 0.0861
.6666 ± .1688
Finally, the 95% Proportion Confidence Interval is [0.4979 , 0.8355]
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