Chapter 7, Problem 1CTC

Critical Thinking Challenges

A confidence interval for a median can be found by using these formulas

$\begin{array}{l}U=\frac{n+1}{2}+\frac{z_{\alpha }/2^{\sqrt{n}}}{2}(roundup)\\ L=n-U+1\end{array}$

to define positions in the set of ordered data values.

Suppose a data set has 30 values, and you want to find the 95% confidence interval for the median. Substituting in the formulas, you get

$\begin{array}{l}U=\frac{30+1}{2}+\frac{1.96\sqrt{30}}{2}=21(roundup)\\ L=30-21+1=10\end{array}$

when n = 30 and zα/2 = 1.96.

Arrange the data in order from smallest to largest, and then select the 10th and 21st values of the data array; hence, X₁₀ < median < X₂₁.

Using the previous information, find the 90% confidence interval for the median for the given data.

84    49    3    133    85    4340    461    60    28    97

14    252    18    16    24    346    254    29    254    6

31    104    72    29    391    19    125    10    6    17

72    31    23    225    72    5    61    366    77    8

26    8    55    138    158    846    123    47    21    82