In a Gallup Poll of 1100 individuals, 495 thought they were worse off financially than a...

In a Gallup Poll of 1100 individuals, 495 thought they were worse off financially than a year ago. Find the 95% confidence interval for the true proportion of individuals
who feel they are worse off financially.

Solutions

Expert Solution

Solution :

Given that,

n = 1100

x = 495

Point estimate = sample proportion = = x / n = 495/1100=0.45

1 - = 1- 0.45 =0.55

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Margin of error = E = Z/2 * $\sqrt$ ((( * (1 - )) / n)

= 1.96 ( $\sqrt$ ((0.45*0.55) /1100 )

E = 0.0294

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.45-0.0294 < p <0.45 +0.0294

0.4206< p < 0.4794

The 95% confidence interval for the population proportion p is : 0.4206, 0.4794

orchestra answered 1 year ago

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