Eight SmartCars were randomly selected and the highway mileage of each was noted. The highway mileage per gallon for each car is shown below: $\begin{array} { l l l l l l l l l } 32 & 42 & 29 & 34 & 41 & 37 & 38 & 39 & 40 \end{array}$
It was desired to determine if the median miles per gallon of all SmartCars exceeded 35 miles per gallon. Identify the test statistic that should be used when conducting the Sign Test.
A) $\mathrm { S } = 2$
B) $S = 8$
C) $\mathrm { S } = 38$
D) $S = 6$

Question

Quizplus · Accepted Answer

The Sign Test is used to test hypotheses about the median of a population when the population is not normally distributed. It is a non-parametric test that compares the median of the sample data to a specified value (in this case, 35 miles per gallon). The test statistic $S$ is the number of sample observations greater than the specified value. In the given data set, six values (37, 38, 39, 40, 41, 42) are greater than 35, so the test statistic $S = 6$.

Eight SmartCars Were Randomly Selected and the Highway Mileage of Each