Question

In
a survey of 2485 adults, 1875 reported that emails are easy to
misinterpret, but only 1214 reported that telephone conversations
are easy to misinterpret.

Construct a 95% confidence interval estimate for the population
proportion of adults who report that emails are easy to
misinterpret.

Construct a 95% confidence interval estimate for the
population proportion of adults who report that telephone
conversations are easy to misinterpret.

Answer #1

a)

Sample Size: 2485

Observed Proportion: 75.45%

Confidence Level: 95%

Confidence Interval:

±1.69

z_{α/2} = 1.9599639861

Lower Bound = p̂ - z_{α/2}•√p̂(1 - p̂)/n = 0.7545 -
(1.9599639861)(0.0086336049717863) = 0.7375784452

Upper Bound = p̂ + z_{α/2}•√p̂(1 - p̂)/n = 0.7545 +
(1.9599639861)(0.0086336049717863) = 0.7714215548

Confidence Interval = (0.7375784452, 0.7714215548)%

Sample Size: 2485

Observed Proportion: 48.85%

Confidence Level: 95%

z_{α/2} = 1.9599639861

Lower Bound = p̂ - z_{α/2}•√p̂(1 - p̂)/n = 0.4885 -
(1.9599639861)(0.010027482356727782) = 0.4688464957

Upper Bound = p̂ + z_{α/2}•√p̂(1 - p̂)/n = 0.4885 +
(1.9599639861)(0.010027482356727782) = 0.5081535043

Confidence Interval = (0.4688464957, 0.5081535043)

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