Respuesta :
(a) sample proportion is 0.75.
(b) The 99% confidence interval for the population proportion is approximately [0.685, 0.815].
(c) a 99% probability that the true population proportion of voters who would support Maria Wilson is within this range.
What is proportion?
A proportion in math is when two ratios are equivalent, that means they are equal to each other.
(a) To calculate the sample proportion, we need to divide the number of voters who would support Maria Wilson by the total sample size. In this case, the sample proportion is 300/400 = 0.75.
(b) To develop a 99% confidence interval for the population proportion, we can use the following formula:
confidence interval = sample proportion +/- (z-value * standard error)
The standard error of the sample proportion is a measure of the variability of the sample proportion, and is calculated as:
[tex]standard\ error = \sqrt{((sample\ proportion * (1 - sample\\ proportion)) / sample size)}\\\\standard\ error= \sqrt{((0.75 * 0.25) / 400)}\\\\standard\ error= 0.025[/tex]
At a 99% confidence level, the z-value is approximately 2.576.
Substituting these values into the formula for the confidence interval, we get:
confidence interval = 0.75 +/- (2.576 * 0.025)
= 0.75 +/- 0.065
= [0.685, 0.815]
So, The 99% confidence interval for the population proportion is approximately [0.685, 0.815].
(c) The confidence interval tells us that we are 99% confident that the population proportion of voters who would support Maria Wilson in the November election is between 0.685 and 0.815. This means that there is a 99% probability that the true population proportion of voters who would support Maria Wilson is within this range.
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