A sample statistic and margin of error are given. Fine the confidence interval likely to contain the population parameter of interest and answer the question
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 Ling. The margin of error was 4.2 percentage points. Should Yin Ling have conceded the election?
A.49.7% to 53.9% no
B. 49.7% to 58.1% no
C. 51.8% to 56% yes
To find the confidence interval, we need to subtract and add the margin of error to the sample statistic.
Lower limit: 53.9% - 4.2% = 49.7%
Upper limit: 53.9% + 4.2% = 58.1%
Therefore, the confidence interval is 49.7% to 58.1%.
Since the confidence interval includes both candidates, Yin Ling should not have conceded the election. The answer is B. 49.7% to 58.1% no.