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Math·Problem-Solving and Data Analysis·Inference from sample statistics and margin of error

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A sample was selected at random from a population. Based on the sample, it is estimated that the mean value of a variable for this population is $178$, with an associated margin of error of $1.5$. Based on the estimate and associated margin of error, which of the following best describes the range of plausible values for the population mean?

A

Any value between $175$ and $178$

B

Any value between $176.5$ and $179.5$

C

Any value less than $176.5$

D

Any value greater than $179.5$