Question

In: Statistics and Probability

Out of 200 people sampled, 12 preferred Candidate A. Based on this, you will estimate what...


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.

[_____ ,_______]

Solutions

Expert Solution

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 )


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