Question

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. bing bing ocene 99% confidence; n = 5900, x = 1770 000 a. 0.00878 b. 0.0117 c. 0.0135 d. 0.0154

Answer 1

Solution :

Given,

n = 5900 ....... Sample size

x = 1770 .......no. of successes in the sample

Let $\hat p$ denotes the sample proportion.

  $\therefore$  $\hat p$ = x/n   = 1770/5900 = 0.3

Our aim is to construct 99% confidence interval.

$\therefore$ c = 0.99

$\therefore$$\alpha$ = 1 - c = 1- 0.99 = 0.01

$\therefore$  $\alpha$/2 = 0.005 and 1- $\alpha$ /2 = 0.995

Search the probability 0.995 in the Z table and see corresponding z value

$\therefore$ = 2.576   

2012

Now , the margin of error is given by

E =  $url=https://latex.codecogs.com/gif.latex?Z&t=1596065046&ymreqid=69d777f6-ff7f-1f97-1c68-8f0002011100&sig=a5EXcv0dFj3Yu8iJ8bNy9w--~D$$\alpha$/2 *  $url=https://latex.codecogs.com/gif.latex?%5Csqrt%7B%5Chat%20p%281-%5Chat%20p%29/n%7D&t=1596065046&ymreqid=69d777f6-ff7f-1f97-1c68-8f0002011100&sig=87L.JK86MS8y65WjS8qKKA--~D$

= 2.576 * $url=https://latex.codecogs.com/gif.latex?%5Csqrt%7B%7D&t=1596065046&ymreqid=69d777f6-ff7f-1f97-1c68-8f0002011100&sig=._SkhVvEPpYpJLwp3sfLlw--~D$ [ 0.3 *(1 - 0.3)/5900]

= 0.0154

Answer : The margin of error is 0.0154

Option d is correct