a researcher is 95% confident that the interval from 19.7 posts to 27.3 posts captures $mu$ = the true mean…

a researcher is 95% confident that the interval from 19.7 posts to 27.3 posts captures $mu$ = the true mean amount of posts high school students make daily on social media. is there evidence that the true mean number of posts high school students make is less than 27? no. there is not evidence for the population mean to be less than 27, because 27 is within the 95% confidence interval. no. there is not evidence for the population mean to be less than 27, because there are values greater than 27 within the 95% confidence interval. yes, there is evidence for the population mean to be less than 27, because 27 is within the 95% confidence interval. yes, there is evidence for the population mean to be less than 27, because 27 is closer to the upper bound of the 95% confidence interval than the lower bound.

a researcher is 95% confident that the interval from 19.7 posts to 27.3 posts captures $mu$ = the true mean amount of posts high school students make daily on social media. is there evidence that the true mean number of posts high school students make is less than 27? no. there is not evidence for the population mean to be less than 27, because 27 is within the 95% confidence interval. no. there is not evidence for the population mean to be less than 27, because there are values greater than 27 within the 95% confidence interval. yes, there is evidence for the population mean to be less than 27, because 27 is within the 95% confidence interval. yes, there is evidence for the population mean to be less than 27, because 27 is closer to the upper bound of the 95% confidence interval than the lower bound.

Answer

Brief Explanations:

A confidence interval gives a range of plausible values for the population mean. If a value (in this case, 27) is within the confidence interval, we cannot conclude that the population mean is less than (or greater than) that value. Just because there are values greater than 27 in the interval (the upper bound is 27.3), we can't say there is evidence the mean is less than 27. The fact that 27 is within the interval means it is a plausible value for the population mean. Saying 27 is closer to the upper bound is not a valid statistical reason for making a conclusion about the population mean being less than 27.

Answer:

No. There is not evidence for the population mean to be less than 27, because 27 is within the 95% confidence interval.