Question

6) A newspaper polls 58 voters to ask which candidate for mayor the supported in an upcoming election.

Of the 58 people polled, 20 said that they intended to vote for Candidate Jones.

a) Find a 99% confidence interval for the true proportion of people in the city who plan to vote for Candidate Jones.

b) Provide the margin of error of the interval as your answer.

Round your answer to 4 decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 20 / 58 = 0.345

1 - = 1 - 0.345 = 0.655

a)

Z/2 = 2.576

b)

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

= 2.576 * (((0.345 * 0.655) / 58)

Margin of error = E = 0.1608

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.345 - 0.1608 < p < 0.345 + 0.1608

0.1842 < p < 0.5058

The 99% confidence interval for the population proportion p is : 0.1842 , 0.5058