Question

Out of 200 people sampled, 12 preferred Candidate A. Based on this, you will estimate what proportion of the voting population (pp) prefers Candidate A.

Use technology to find a 90% confidence level, and give your answers as decimals, to four places.

[_____ ,_______]

Answer 1

Solution =   

Given,

n = 200 ....... Sample size

x = 12 .......no. of successes in the sample

Let denotes the sample proportion.

     = x/n   = 12 / 200 = 0.06

Our aim is to construct 90% confidence interval.

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05 and 1- /2 = 0.950

= 1.645 (use z table)

Now , the margin of error is given by

E =   *  

= 1.645 * [ 0.06 *(1 - 0.06)/ 200]

= 0.0276

Now the confidence interval is given by

( - E)   ( + E)

( 0.06 - 0.0276 )   ( 0.06 + 0.0276 )

0.0324   0.0876

Required 90% Confidence Interval is ( 0.0324 , 0.0876 )