Question

based on a random sample from a population, a researcher estimated that the mean value of a certain variable for the population is 20.5, with an associated margin of error of 1. which of the following is the most appropriate conclusion?
a it is plausible that the actual mean value of the variable for the population is between 19.5 and 21.5.
b it is not possible that the mean value of the variable for the population is less than 19.5 or greater than 21.5.
c every value of the variable in the population is between 19.5 and 21.5.
d the mean value of the variable for the population is 20.5.

Explanation:

Step1: Recall the formula for confidence interval

The confidence interval is given by \(\text{Estimated mean}\pm\text{Margin of error}\). Here, the estimated mean is \(20.5\) and the margin of error is \(1\).

Step2: Calculate the confidence interval

The lower - bound of the confidence interval is \(20.5 - 1=19.5\) and the upper - bound is \(20.5 + 1 = 21.5\). A confidence interval gives a range of values within which the True population parameter (in this case, the population mean) is likely to lie.

Answer:

A. It is plausible that the actual mean value of the variable for the population is between 19.5 and 21.5.