In: Statistics and Probability
Suppose a man tasted 20 cups of coffee and got correct 75% of the time. What will be the confidence interval of her correctness at 95%, 99%, and 99.9%.
Sample proportion = 0.75
Sample size (n) = 20
Confidence interval(in %) = 95
z @ 95% = 1.96
Since we know that
Required confidence interval = (0.75-0.1897, 0.75+0.1897)
Required confidence interval = (0.5603, 0.9397)
Confidence interval(in %) = 99
z @ 99% = 2.576
Since we know that
Required confidence interval = (0.75-0.2494, 0.75+0.2494)
Required confidence interval = (0.5006, 0.9994)
Confidence interval(in %) = 99.9
z @ 99.9% = 3.291
Since we know that
Required confidence interval = (0.75-0.3186, 0.75+0.3186)
Required confidence interval = (0.4314, 1.0686)
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