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. 175.6 - 13.9 < μ < 175.6 + 13.9
d. 161.7 ± 27.8

Explanation:

Step1: Calculate the mid - point and margin of error

The mid - point of the confidence interval \(161.7\lt\mu\lt189.5\) is \(\frac{161.7 + 189.5}{2}=\frac{351.2}{2}=175.6\).
The margin of error \(E\) is \(\frac{189.5 - 161.7}{2}=\frac{27.8}{2}=13.9\).

Step2: Analyze each option

• Option A: \((161.7,189.5)\) is the original confidence interval, so it is equivalent.
• Option B: \(\mu=175.6\pm13.9\) means \(175.6 - 13.9\lt\mu\lt175.6 + 13.9\), which is equivalent to \(161.7\lt\mu\lt189.5\).
• Option C: \(175.6 - 13.9\lt\mu\lt175.6 + 13.9\) is equivalent to \(161.7\lt\mu\lt189.5\).
• Option D: \(161.7\pm27.8\) means \(161.7-27.8 = 133.9\) and \(161.7 + 27.8=189.5\), which is \(133.9\lt\mu\lt189.5\), not equivalent to \(161.7\lt\mu\lt189.5\).

Answer:

D. \(161.7\pm27.8\)