Question

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

Explanation:

Step1: Calculate the sample mean

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

Step2: Calculate the margin of error

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

Step3: Analyze each option

• Option A: The interval $(161.7,189.5)$ is just another way of writing $161.7<\mu<189.5$
• Option B: $175.6\pm13.9$ means $175.6 - 13.9<\mu<175.6 + 13.9$. Since $\bar{x}=175.6$ and $E = 13.9$, this is equivalent.
• Option C: If we have $161.7\pm27.8$, then the interval is $161.7-27.8<\mu<161.7 + 27.8$, i.e., $133.9<\mu<189.5$, which is not equivalent to $161.7<\mu<189.5$
• Option D: $175.6 - 13.9<\mu<175.6 + 13.9$ is equivalent to $161.7<\mu<189.5$ as we calculated above.

Answer:

C. \(161.7\pm27.8\)