A poll conducted the day before the student body presidential election at a midwestern university showed that 53.9 percent favored Mario, the rest favoring yin lang. the margin of error was 4.2 percent points. Should yin lang have conceded the election? A sample statistic and margin and error are given Find the confidence interval likely to contain the population parameter of interest and answer the question
To find the confidence interval, we need to calculate the upper and lower bounds using the given sample statistic, margin of error, and confidence level.
Given:
Sample statistic (p̂) = 53.9%
Margin of error (E) = 4.2%
Confidence level (C) = Since it is not mentioned in the question, we will assume a common confidence level of 95%.
First, convert the given margin of error from a percentage to a decimal:
Margin of error (E) = 4.2% = 0.042
Next, calculate the lower and upper bounds of the confidence interval using the formula:
Lower bound = Sample statistic - Margin of error
Upper bound = Sample statistic + Margin of error
Lower bound = 53.9% - 0.042 = 0.539 - 0.042 = 0.497
Upper bound = 53.9% + 0.042 = 0.539 + 0.042 = 0.581
The confidence interval is likely to contain the true population parameter, which represents the proportion of favorability towards Mario. In this case, the confidence interval is (0.497, 0.581).
To answer the question of whether Yin Lang should have conceded the election, more information is needed, such as the proportion of favorability towards Yin Lang. If the lower bound of the confidence interval for Yin Lang is higher than the upper bound for Mario, then Yin Lang may have had a chance of winning. However, specific values for Yin Lang are not provided in the question.
To find the confidence interval, we need to consider the sample proportion and the margin of error.
The sample proportion in favor of Mario is 53.9%. The margin of error is ±4.2 percentage points.
To calculate the confidence interval, we can use the following formula:
Confidence Interval = Sample Proportion ± Margin of Error
Plugging in the values, we get:
Confidence Interval = 53.9% ± 4.2%
To find the lower bound of the confidence interval, subtract the margin of error from the sample proportion:
Lower Bound = 53.9% - 4.2%
Lower Bound = 49.7%
To find the upper bound of the confidence interval, add the margin of error to the sample proportion:
Upper Bound = 53.9% + 4.2%
Upper Bound = 58.1%
Therefore, the confidence interval likely to contain the population parameter of interest is 49.7% to 58.1%.
As for whether Yin Lang should have conceded the election, we cannot make a definitive statement based solely on the given information. The confidence interval accounts for the potential margin of error, so it is possible that Yin Lang's actual support could be within this range. However, any decision to concede would also depend on other factors such as the number of votes, campaign strategies, and overall confidence in the polling data.
To find the confidence interval likely to contain the population parameter of interest (in this case, the proportion of people favoring Yin Lang), we can use the sample statistic and the margin of error provided.
Given:
Sample proportion (p̂) = 53.9% = 0.539 (favoring Mario)
Margin of error (ME) = 4.2% = 0.042
We need to determine the confidence level, which is not explicitly mentioned in the question. Let's assume a 95% confidence level, which is commonly used.
Now, to calculate the confidence interval, we can use the following formula:
Confidence Interval = Sample Proportion ± (Z * Standard Error)
Where Z is the appropriate z-score for the desired confidence level and Standard Error (SE) can be calculated using the formula:
SE = √((p̂*(1-p̂))/n)
In this case, n (sample size) is not provided, so we cannot calculate the exact confidence interval without additional information. However, we can still answer the question based on the given information.
Considering the margin of error of 4.2 points, we can conclude that the actual proportion of people favoring Yin Lang lies within the range:
(0.539 - 0.042, 0.539 + 0.042) or (0.497, 0.581)
Since the lower bound of the confidence interval is greater than zero, it indicates that there is still a chance that Yin Lang could have won the election. Therefore, it cannot be definitively concluded that Yin Lang should have conceded the election based solely on this information.