Question
In: Statistics and Probability
A survey of 865 voters in one state reveals that 408 favor approval of an issue....
A survey of 865 voters in one state reveals that 408 favor approval of an issue. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval.
A) 0.444 < p < 0.500
B) 0.471 < p < 0.472
C) 0.438 < p < 0.505
D) 0.435 < p < 0.508
Solutions
Expert Solution
Solution :
Given that,
n = 865
x = 408
Point estimate = sample proportion = 
= x / n = 0.472
1 -
= 0.528
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2
= Z0.025 = 1.96
Margin of error = E = Z
/ 2 * 
* (1 -
)) / n)
= 1.96 * (
= 0.033
A 95% confidence interval for population proportion p is ,
- E < p <
+ E
0.472 - 0.033 < p < 0.472 + 0.033
0.438 < p < 0.505
Option c is correct.
orchestra answered 1 year agoRelated Solutions
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