Question

score: 1/10 penalty: 1 off
question
a study was commissioned to find the mean weight of the residents in a certain town. the study found the mean weight to be 179 pounds with a margin of error of 10 pounds. which of the following is a reasonable value for the true mean weight of the residents of the town?
answer
166.5 184.9
168.5 189.5

Explanation:

Step1: Determine the confidence - interval range

The sample mean is 179 pounds and the margin of error is 10 pounds. The confidence - interval for the true mean $\mu$ is given by $\bar{x}-E\leq\mu\leq\bar{x} + E$, where $\bar{x}$ is the sample mean and $E$ is the margin of error. So, the lower limit is $179 - 10=169$ pounds and the upper limit is $179+10 = 189$ pounds.

Step2: Check each option

We check which of the given values lies within the interval $[169,189]$.

• For 166.5, since $166.5<169$, it is not in the interval.
• For 168.5, since $168.5<169$, it is not in the interval.
• For 184.9, since $169\leq184.9\leq189$, it is in the interval.
• For 189.5, since $189.5>189$, it is not in the interval.

Answer:

184.9