Question

In: Statistics and Probability

Suppose a man tasted 20 cups of coffee and got correct 75% of the time. What...

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%.

Solutions

Expert Solution

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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