Question

In a survey of 2598 adults in a recent year, 1383 say they have made a new years resolution

Construct​ 90% and​ 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals

Answer 1

90% confidence interval is

z_α/2 = 1.645

Lower Bound = p̂ - z_α/2•√p̂(1 - p̂)/n

=0.5323 - (1.645)(0.0098)

= 0.5162

Upper Bound = p̂ + z_α/2•√p̂(1 - p̂)/n

= 0.5323 + (1.645)(0.0098)

= 0.548

Confidence Interval = (0.5162, 0.5484)

95% confidence interval is

z_α/2 = 1.959

Lower Bound = p̂ - z_α/2•√p̂(1 - p̂)/n

= 0.5323 - (1.96)(0.0098)

= 0.5131

Upper Bound = p̂ + z_α/2•√p̂(1 - p̂)/n

= 0.5323 + (1.96)(0.0098)

= 0.5515

Confidence Interval = (0.5131, 0.5515)

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