Problem 6. (Lunar Rocks) [10 pts] It is believed that rocks on the moon are olde
ID: 3271287 • Letter: P
Question
Problem 6. (Lunar Rocks) [10 pts] It is believed that rocks on the moon are older than rocks on earth. In order to find out if this is the case, a team of astrologists collect a sample of 10 lunar rocks (gathered randomly from a recent mission to the Moon), and a sample of 10 earth rocks, collected randomly from all over the planet. Below is a table that lists the age of each rock (in billions of years):
(a) Assume that the two rock samples are independent. Perform a Wilcoxon-Mann-Whitney Test to assess whether lunar rocks are older than earth rocks.
(b) Now assume that the two rock samples are paired (by observation number). Perform a Sign Test to assess the same question as in (a).
Explanation / Answer
By using MINITAB
a]
Choose Stat > Nonparametrics > Mann-Whitney.
In First Sample, enter DBP1. In Second Sample, enter DBP2. Click OK.
Session window output
MTB > Mann-Whitney 95.0 'Lunar rock' 'Earth rock';
SUBC> Alternative 1.
Mann-Whitney Test and CI: Lunar rock, Earth rock
N Median
Lunar rock 10 2.750
Earth rock 10 2.950
Point estimate for ETA1-ETA2 is -0.200
95.5 Percent CI for ETA1-ETA2 is (-1.300,1.000)
W = 101.5
Test of ETA1 = ETA2 vs ETA1 > ETA2
Cannot reject since W is < 105.0
Conclusion:
At 5% level of significant, we can not claim that the Lunar rock is older than Earth rock.
b]
MTB > SInterval 95.0 'Lunar rock' 'Earth rock'.
Sign CI: Lunar rock, Earth rock
Sign confidence interval for median
Achieved Confidence Interval
N Median Confidence Lower Upper Position
Lunar rock 10 2.750 0.8906 2.100 3.300 3
0.9500 1.963 3.403 NLI
0.9785 1.700 3.600 2
Earth rock 10 2.950 0.8906 2.000 3.800 3
0.9500 1.829 3.834 NLI
0.9785 1.500 3.900 2
MTB > STest 0.0 'Lunar rock' 'Earth rock';
SUBC> Alternative 0.
Sign Test for Median: Lunar rock, Earth rock
Sign test of median = 0.00000 versus not = 0.00000
N Below Equal Above P Median
Lunar rock 10 0 0 10 0.0020 2.750
Earth rock 10 0 0 10 0.0020 2.950