Question

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

1. What hypothesis should be run to determine if there is a significant association between stiffness and temperature?
2. Run the appropriate test is Minitab and show the Minitab output.
3. State your conclusions about the strength of this relationship if we use a 5% level of significance.
4. Are these conclusions supported by the R² value for this relationship? Explain.

Answer 1

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.