The sample mean of the variable height in a data set was found to be 68 inches, with a standard error of four inches. The researcher reported that the population or true mean height fell within one margin of error of the sample mean, at the 95% confidence level. What is the chance that the true mean is 75 inches or more?
A) 95%
B) 2.5%
C) 5%
D) 47.5%

Question

Quizplus · Accepted Answer

Given the 95% confidence interval, the true mean is within one margin of error (±4 inches) of the sample mean (68 inches). This means the interval is from 64 to 72 inches. A true mean of 75 inches or more is outside this interval, which corresponds to the tails of the distribution (2.5% on each tail for a 95% confidence interval). Therefore, the chance that the true mean is 75 inches or more is 2.5%.

The Sample Mean of the Variable Height in a Data