Question

In: Statistics and Probability

Nine hundred registered voters are surveyed before a presidential election. Four hundred and eightysix say they...

Nine hundred registered voters are surveyed before a presidential election. Four hundred and eightysix say they will vote for candidate X. Construct a 95% confidence interval for the proportion of registered voters who will vote for candidate X.

Expert Solution

Solution :

Given that,

n = 900

x = 480

Point estimate = sample proportion = = x / n = 480/900=0.533

1 - = 1- 0.533 =0.467

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 ( $\sqrt$ ((0.533*0.467) /900 )

E = 0.0326

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.533-0.0326 < p <0.533+ 0.0326

0.5004< p < 0.5656

The 95% confidence interval for the population proportion p is : 0.5004, 0.5656

orchestra answered 3 years ago

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