Respuesta :
Answer:
C. 67.5 to 72.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The width of the interval is determined by it's margin of error, which is given by the following formula:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
So, as n increases, the margin of error decreases, and the interval gets smaller.
Using 10,000 bootstrap samples for the distribution:
We increase the sample size, which means that the interval gets smaller.
We had 67 to 73, since it got smaller, it will be from a value higher than 67 to a value lower than 73.
So the correct answer is:
C. 67.5 to 72.
The degree of uncertainty or certainty is the confidence interval. From the following confidence intervals, C is the most likely result after the change which is 67.5 to 72.
What is a confidence interval?
A confidence interval depicts the likelihood that a parameter will fall between two values near the mean.
The degree of uncertainty or certainty in a sampling process is measured by confidence intervals. They are often built with confidence levels of 95 percent or 99 percent.
The confidence interval is given as ;
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n} }[/tex]
z score is denoted by z
The margin of error is helpful to find the width of the interval which is determined by the following formula;
[tex]M= z\sqrt{\frac{\pi(1-\pi)}{n} }[/tex]
The value of n is inversly propotional to the margin of error. If the value of n increases, the margin of error decreases, and also the interval gets decreases.
Using 10,000 bootstrap samples for the distribution:
As the valuer of sample size increases the interval gets smaller values.
We had 67 to 73 given in the problem it will be from a value greater than 67 to a value lower than 73.
From all the observations we come to the conclusion that C is the most likely result after the change which is 67.5 to 72.
Hence C is the most appropriate answer
To learn more about the confidence interval refer the link;
https://brainly.com/question/2396419
