Problem 6. (Lunar Rocks) [10 pts] It is believed that rocks on the moon are olde

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).

Observation Number 1 2 3 4 5 6 7 8 9 10 Lunar rock 2.1 3.6 2.4 3.3 6.1 1.7 0.8 2.5 3.0 3.2 Earth Rock 2.0 3.9 2.6 3.4 5.5 1.5 0.7 2.9 3.8 3.0

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

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