Out of 600 people sampled, 228 preferred Candidate A. Based on this, estimate what proportion of the voting population ( π π ) prefers Candidate A. Use a 90% confidence level, and give your answers as decimals, to three places. < π π
Solution :
Given that,
Point estimate = sample proportion =
= x / n = 228 / 600 = 0.380
1 -
= 1 - 0.380 = 0.62
Z/2
= 1.645
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 1.645 * (((0.380
* 0.62) / 600)
Margin of error = E = 0.033
A 90% confidence interval for population proportion p is ,
- E <
<
+ E
0.380 - 0.033 <
< 0.380 + 0.033
0.347 <
< 0.413
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