Question

which of the following is not an equivalent expression for the confidence interval given by $161.7<\mu <189.5$?
choose the correct answer below
a. $175.6\pm 13.9$
b. $175.6 - 13.9<\mu <175.6 + 13.9$
c. $161.7\pm 27.8$
d. $(161.7,189.5)$

Explanation:

Step1: Calculate the sample mean $\bar{x}$

The sample mean $\bar{x}=\frac{161.7 + 189.5}{2}=\frac{351.2}{2}=175.6$

Step2: Calculate the margin of error $E$

The margin of error $E=\frac{189.5 - 161.7}{2}=\frac{27.8}{2}=13.9$

Step3: Analyze each option

• Option A: $175.6\pm13.9$ is equivalent to $175.6 - 13.9<\mu<175.6 + 13.9$ which is the same as the original interval.
• Option B: $175.6 - 13.9<\mu<175.6 + 13.9$ is equivalent to the original interval.
• Option C: $161.7\pm27.8$ is $161.7-27.8 = 133.9$ and $161.7 + 27.8=189.5$, but the center of this interval is $161.7$ instead of $175.6$.
• Option D: $(161.7,189.5)$ is the same as the original interval $161.7<\mu<189.5$

Answer:

C. $161.7\pm27.8$