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)