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 margin - of - error concept

The confidence interval for the population mean is given by $\text{Sample Mean}\pm\text{Margin of Error}$.

Step2: Calculate the confidence interval

Given sample mean $\bar{x}=20.5$ and margin of error $E = 1$. The lower limit of the confidence interval is $\bar{x}-E=20.5 - 1=19.5$ and the upper limit is $\bar{x}+E=20.5 + 1=21.5$. This means it is plausible that the actual population mean lies within this interval.

Answer:

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