Question

Cyberbullying rates: Teens were surveyed about cyberbullying, and a 95% confidence interval for the percentage of teens who report experiencing cyberbullying is 54% to 66%. Answer the following questions based on this interval.

A researcher conjectured that 65% of all teens have experienced cyberbullying. Is this claim reasonable based on the confidence interval? Explain your reasoning.

A.Yes, since 65% is contained in the confidence interval, it is a plausible value for the population percentage.
B.No, since 65% is pretty close to the upper end of the confidence interval, the actual population percentage is probably lower than 65%.
C,No, the actual population percentage is probably higher than 65%

Answer 1

The conjecture that 65% of all teens have experienced cyberbullying is reasonable because 65% is within the 95% confidence interval of 54% to 66%. The correct answer is option A.

Step-by-step explanation:

The conjecture that 65% of all teens have experienced cyberbullying is reasonable based on the 95% confidence interval provided, which ranges from 54% to 66%. This is because 65% falls within the given interval. We interpret the confidence interval to mean that we are 95% sure that the true percentage of teens who experience cyberbullying in the entire population lies between 54% and 66%. Since 65% is within this range, it is a plausible value for the actual population percentage.

Therefore, the correct answer to the question is: A. Yes, since 65% is contained in the confidence interval, it is a plausible value for the population percentage.