Pollution Control Two types of instruments for measuring the amount of sulfur mo
ID: 3333722 • Letter: P
Question
Pollution Control
Two types of instruments for measuring the amount of sulfur monoxide in the atmosphere are being compared in an air-pollution experiment. The data set below contains the readings of sulfur monoxide that were recorded by each of the instruments each day for a period of two weeks. The variables are day, instrA and instrB which contain respectively the day the reading was made and the level of sulfur monoxide recorded by instrument A and instrument B respectively.
a.) Use the sign test to test whether the two instrument readings are the same.
b.) Use the rank-sign test to test whether the two instrument readings are the same.
c.) Are there any differences in the conclusions of the two tests?
d.) When might we get two different conclusions from the sign test and the rank-sign test if we are
using the same data set?
Explanation / Answer
a)
b)
c)
No, there are no differences in the conclusions of the two tests.
d)
There are possibilities when the sample is large enough as that might affect both calculated value and critical value.
Day InstrA InstrB InstrA-InstrB Sign 1 0.96 0.87 0.09 + 2 0.82 0.74 0.08 + 3 0.75 0.63 0.12 + 4 0.61 0.55 0.06 + 5 0.89 0.76 0.13 + 6 0.64 0.7 -0.06 - 7 0.81 0.69 0.12 + 8 0.68 0.57 0.11 + 9 0.65 0.53 0.12 + 10 0.84 0.88 -0.04 - 11 0.59 0.51 0.08 + 12 0.94 0.79 0.15 + 13 0.91 0.84 0.07 + 14 0.77 0.63 0.14 + 2 Negatives 12 Positives 0.999 p-value using binomial distribution with p=0.5, x=12 and n=14 p-value is greater than a and hence we cannot reject the null hypothesis