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A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be 153 pounds with a margin of error of 5 pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town?
148.5
149.1
156
158.5

A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be $153$ pounds with a margin of error of $5$ pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town? $\newline$ $148$ . $5$ $\newline$ $149$ . $1$ $\newline$ $156$ $\newline$ $158$ . $5$

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Interpret confidence intervals for population means

Full solution

Q. A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be

153

pounds with a margin of error of

5

pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town?

\newline

148

.

5

\newline

149

.

1

\newline

156

\newline

158

.

5

Calculate range of values: Calculate the range of reasonable values for the true mean weight using the given margin of error. $\newline$ The margin of error is $5$ pounds, which means the true mean weight could reasonably be $5$ pounds less than or $5$ pounds more than the reported mean weight of $153$ pounds. $\newline$ Lower limit = Mean weight - Margin of error $\newline$ = $153 - 5$ $\newline$ = $148$
Calculate upper limit: Calculate the upper limit of the reasonable values for the true mean weight. $\newline$ Upper limit = Mean weight + Margin of error $\newline$ = $153 + 5$ $\newline$ = $158$
Determine range of values: Determine the range of reasonable values for the true mean weight. The reasonable values for the true mean weight are between $148$ and $158$ pounds, inclusive.
Compare with range: Compare each given value with the range of reasonable values to find the outlier. $\newline$ - $148.5$ is within the range $(148$ to $158)$ , so it is a reasonable value. $\newline$ - $149.1$ is within the range $(148$ to $158)$ , so it is a reasonable value. $\newline$ - $156$ is within the range $(148$ to $158)$ , so it is a reasonable value. $\newline$ - $158.5$ is outside the range $(148$ to $158)$ , so it is not a reasonable value.

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