Respuesta :
The voter preference for the incumbent has a 95% confidence interval of 0.071 to 0.129.
What do we mean by confidence interval?
A confidence interval is a range of values that are bound by the statistic's mean and that is likely to include an unidentified population parameter.
The proportion of probability, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.
So, we have the following confidence interval of proportions for a sample of n people who were surveyed with a success chance of π and a confidence interval of 1-a.
[tex]\pi \pm z \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
When the z-score has a p-value of a, it is designated as b 1 - a/2.
We have this in relation to the issue:
A sample of 400 voters revealed that 360 supported the current governor. This indicates that the current governor is not in favor because 400-360 = 40.
So:
n = 400, π = 40/400 = 0.1
Now, the interval's lower limit is:
[tex]\pi-z \sqrt{\frac{\pi(1-\pi)}{n}}=0.10-1.96 \sqrt{\frac{0.10 * 0.90}{400}}=0.071[/tex]
This range's maximum value is:
[tex]\pi+z \sqrt{\frac{\pi(1-\pi)}{n}}=0.10+1.96 \sqrt{\frac{0.10 * 0.90}{400}}=0.129[/tex]
Therefore, the voter preference for the incumbent has a 95% confidence interval of 0.071 to 0.129.
Know more about the confidence interval here:
https://brainly.com/question/17097944
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