In: Statistics and Probability
A materials engineer at a furniture manufacturing site wants to assess the stiffness of the particle board that the manufacturer uses. The engineer collects stiffness data from particle board pieces that have various densities at different temperatures. Data are found in the file Particle Board Stiffness.
Density | Stiffness | Temp |
9.5 | 14.81 | 70.6 |
8.4 | 17.50 | 73.3 |
9.8 | 14.01 | 66.2 |
11 | 19.44 | 70.1 |
8.3 | 7.57 | 69.3 |
9.9 | 14.19 | 69.1 |
8.6 | 9.71 | 69.8 |
6.4 | 8.08 | 64.4 |
7 | 5.30 | 65.4 |
8.2 | 10.73 | 67.8 |
17.4 | 43.24 | 69.7 |
15 | 25.32 | 66.9 |
15.2 | 28.03 | 71.5 |
16.4 | 41.79 | 66.6 |
16.7 | 49.50 | 68.0 |
15.4 | 25.31 | 64.3 |
15 | 26.22 | 64.5 |
14.5 | 22.15 | 71.3 |
14.8 | 26.75 | 69.6 |
13.6 | 18.04 | 71.1 |
25.6 | 96.31 | 72.1 |
24.4 | 72.59 | 67.3 |
23.3 | 49.51 | 66.7 |
19.5 | 32.21 | 68.1 |
21.2 | 48.22 | 66.5 |
22.8 | 70.45 | 65.7 |
21.7 | 47.66 | 66.3 |
19.8 | 38.14 | 69.4 |
21.3 | 53.05 | 68.3 |
Minitab output,
Welcome to Minitab, press F1 for help.
MTB > Correlation 'Stiffness' 'Temp'.
Correlation: Stiffness, Temp
Pearson correlation of Stiffness and Temp = -0.001
P-Value = 0.995
___________________________________________________________________________________________________
a)
The hypothesis to determine if there is a significant
association between stiffness and temperature is,
Ho : There is no significant association between stiffness and
temperature.
Ha : There is a significant association between stiffness and
temperature.
b)
We use correlation test in Minitab,(see output of the test
above)
c)
From minitab output, Observe that correlation of Stiffness and Temp
= -0.001.
The P-value = 0.995 > alpha = 0.05, idicates that there is no
significant association between stiffness and temperature.
d) yes these conclusions supported by the R2 value for this
relationship because,
R2 = - 0.0001 which is nearly equal to 0 means there is no
correlation.