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

Answer 1

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.