Question

In a random sample of 750 voters exiting Dallas polls, 450 claimed to have voted for the constitutional amendment banning marriage for two individuals of the same sex. Construct a 99% confidence interval estimate of the proportion of votes for this constitutional amendment in Dallas.

A. 57% - 63%

B. 55% - 65%

C. 56% - 64%

D. None of the above

Answer 1

Solution :

Given that,

n = 750

x = 450

Point estimate = sample proportion = = x / n = 450/750=0.6

1 -   = 1-0.6 =0.4

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

= 2.576* (((0.6*0.4) /750 )

E = 0.046

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.6-0.046 < p < 0.6+0.046

0.55< p < 0.65

55% - 65%