A quality control supervisor wishes to determine whether the following measurements are random: $$\begin{array}{l}
\begin{array} { r r r r r r r r }
68.2 & 65 & 66.5 & 65 & 67.5 & 68 & 66 & 64.5 \
65.3 & 64.2 & 67.6 & 66.5 & 66.8 & 68.9 & 67 & 65 \
\hline\
\end{array}\
\begin{array} { r r r r r r r | }
\hline 65 & 67 & 68 & 71 & 68.5 & 63.6 & 64.7 \
71.5 & 70.7 & 66 & 68.5 & 70.5 & 69.5 & 70.1 \
\hline
\end{array}
\end{array}$$ For this purpose, the supervisor uses a previous median of 67.9 and compares each measurement to the median to perform a runs test.She uses a significance level of 0.05.The appropriate decision is ______.
A)reject the null hypothesis and conclude that the observations are random
B)reject the null hypothesis and conclude that the observations are not random
C)do not reject the null hypothesis and conclude that the observations are random
D)do not reject the null hypothesis and conclude that the observations are not random
E)do nothing

Question

A quality control supervisor wishes to determine whether the following measurements are random: $$\begin{array}{l}
\begin{array} { r r r r r r r r } 
68.2 & 65 & 66.5 & 65 & 67.5 & 68 & 66 & 64.5 \
65.3 & 64.2 & 67.6 & 66.5 & 66.8 & 68.9 & 67 & 65 \
\hline\
\end{array}\
\begin{array} { r r r r r r r | } 
\hline 65 & 67 & 68 & 71 & 68.5 & 63.6 & 64.7 \
71.5 & 70.7 & 66 & 68.5 & 70.5 & 69.5 & 70.1 \
\hline
\end{array}
\end{array}$$ For this purpose, the supervisor uses a previous median of 67.9 and compares each measurement to the median to perform a runs test.She uses a significance level of 0.05.The appropriate decision is ______.
A)reject the null hypothesis and conclude that the observations are random
B)reject the null hypothesis and conclude that the observations are not random
C)do not reject the null hypothesis and conclude that the observations are random
D)do not reject the null hypothesis and conclude that the observations are not random
E)do nothing

Quizplus · Accepted Answer

The runs test is used to determine if a sequence of data points is random. If the test statistic falls within the critical values for a given significance level, we do not reject the null hypothesis, which states that the sequence is random. Since the specific test statistic and critical values are not provided, the general approach to a runs test would lead to either not rejecting or rejecting the null hypothesis based on how the data compares to the median. Without the exact calculations or results, the most appropriate conclusion based on the information given would be that we do not reject the null hypothesis, suggesting that the observations could be random, assuming the test statistic does not indicate a significant departure from randomness.

A Quality Control Supervisor Wishes to Determine Whether the Following