Holooly Plus Logo
Holooly Plus Logo

Question 4.DS.15: A fastener tool lab conducts a study to compare the amount o......

A fastener tool lab conducts a study to compare the amount of powder coating of dry thread adhesive applied to prevailing torque fasteners from two different manufacturers. Historical data shows that the distribution of powder coating of the adhesive from both manufacturers is approximately normal but the variances differ. A random sample of adhesive coatings is tested and yields the following:

The tool lab decides to test the hypothesis that \sigma ^{2}_{1}=\sigma ^{2}_{2} against the alternative that \sigma ^{2}_{1} > \sigma ^{2}_{2}, using a 0.05 level of significance.

Manufacturer A Manufacturer B
n_{1} = 16 n_{2} = 18
S_{1} = 7.2 S_{2} = 6.4
Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.
Report Answer

Approach:

1.H_{0}:\sigma ^{2}_{1}=\sigma ^{2}_{2}, H_{A}:  \sigma ^{2}_{1} > \sigma ^{2}_{2}

2. \alpha = 0.05  ∂_{1}=n_{1}-1=16-1=15  ∂_{2}=n_{2}-1=18-1=17

3. From the data and Table 4.7 the lab finds f_{a} (∂_{1},  ∂_{2}) = f_{0.05}(15,17)=2.31

4. Analysis F =S^{2}_{1}/S^{2}_{2}=\frac{\left(7.2\right)^{2} }{\left(6.4\right)^{2} }=1.27

Displaying this data on a sketch reveals the following:

Since we find F = 1.27 to be less than F_{0.05}(15,17) = 2.31 there is insufficient information to reject H_{0} hence \sigma ^{2}_{1}=\sigma ^{2}_{2}.

Therefore, the lab concludes that there is no variation in the distribution of dry adhesive thread coating from the two manufacturers.

TABLE 4.7
Percentiles of the F-Distribution F.95 (∂1 , ∂2 )   
∂1
∂2		 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞
1 39.86 49.5 58.59 56.88 57.24 58.2 58.91 59.44 59.86 60.19 60.71 61.22 61.74 62 62.26 62.58 62.79 63.06 68.33
2 8.53 9 9.16 9.24 9.29 9.33 9.35 9.37 9.38 9.39 9.41 9.42 9.44 9.45 9.46 9.47 9.47 9.48 9.49
3 5.54 6.46 6.39 5.34 5.31 5.28 5.27 5.25 5.24 5.23 5.22 5.2 5.18 5.18 5.17 5.16 5.15 5.14 5.13
4 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94 3.92 3.9 3.87 3.84 3.88 3.82 3.8 3.79 3.78 3.76
5 4.06 3.78 3.62 3.52 3.45 3.4 3.37 3.34 3.32 3.3 3.27 3.24 3.21 3.19 3.17 3.15 3.14 3.12 3.1
6 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96 2.94 2.9 2.87 2.84 2.82 2.8 2.78 2.76 2.74 2.72
7 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72 2.7 2.67 2.68 2.59 2.58 2.56 2.54 2.51 2.49 2.47
8 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56 2.6 2.5 2.46 2.42 2.4 2.38 2.36 2.34 2.32 2.29
9 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44 2.42 2.38 2.34 2.3 2.28 2.25 2.23 2.21 2.18 2.16
10 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.88 2.35 2.32 2.28 2.24 2.2 2.18 2.16 2.13 2.11 2.08 2.06
11 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.3 2.27 2.25 2.21 2.17 2.12 2.1 2.08 2.05 2.03 2 1.97
12 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21 2.19 2.15 2.1 2.06 2.04 2.01 1.99 1.96 1.98 1.9
13 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.2 2.16 2.14 2.1 2.05 2.01 1.98 1.96 1.93 1.9 1.88 1.85
14 3.1 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12 2.1 2.05 2.01 1.96 1.94 1.91 1.89 1.86 1.83 1.8
15 3.07 2.7 2.49 2.36 2.27 2.21 2.16 2.12 2.09 2.06 2.02 1.97 1.92 1.9 1.87 1.85 1.82 1.79 1.76
16 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06 2.03 1.99 1.94 1.89 1.87 1.84 1.81 1.78 1.76 1.72
17 3.03 2.64 2.44 2.31 2.22 2.15 2.1 2.06 2.03 2 1.96 1.91 1.86 1.84 1.81 1.78 1.75 1.72 1.69
18 3.01 2.62 2.42 2.29 2.2 2.13 2.08 2.04 2 1.98 1.93 1.89 1.84 1.81 1.78 1.75 1.72 1.69 1.68
19 2.99 2.61 2.4 2.27 2.18 2.11 2.06 2.02 1.98 1.96 1.91 1.86 1.81 1.79 1.76 1.73 1.7 1.67 1.63
20 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2 1.96 1.94 1.89 1.84 1.79 1.77 1.74 1.71 1.68 1.64 1.61
21 2.96 2.57 2.36 2.23 2.14 2.08 2.02 1.98 1.95 1.92 1.87 1.83 1.78 1.75 1.72 1.69 1.66 1.62 1.59
22 2.95 2.56 2.35 2.22 2.13 2.06 2.01 1.97 1.93 1.9 1.86 1.81 1.76 1.73 1.7 1.67 1.64 1.6 1.57
23 2.94 2.55 2.34 2.21 2.11 2.05 1.99 1.95 1.92 1.89 1.84 1.8 1.74 1.72 1.69 1.66 1.62 1.58 1.55
24 2.93 2.54 2.33 2.19 2.1 2.04 1.98 1.94 1.91 1.88 1.83 1.78 1.73 1.7 1.67 1.64 1.61 1.57 1.53
25 2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1.89 1.87 1.82 1.77 1.72 1.69 1.66 1.63 1.59 1.56 1.52
26 2.91 2.52 2.31 2.17 2.08 2.01 1.96 1.92 1.88 1.86 1.81 1.76 1.71 1.68 1.65 1.61 1.58 1.54 1.5
27 2.9 2.51 2.3 2.17 2.07 2 1.95 1.91 1.87 1.85 1.8 1.75 1.7 1.67 1.64 1.6 1.57 1.53 1.49
28 2.89 2.5 2.29 2.16 2.06 2 1.94 1.9 1.87 1.84 1.79 1.74 1.69 1.66 1.63 1.59 1.56 1.52 1.48
29 2.89 2.5 2.28 2.15 2.06 1.99 1.93 1.89 1.86 1.83 1.78 1.73 1.68 1.65 1.62 1.58 1.55 1.51 1.47
30 2.88 2.49 2.28 2.14 2.06 1.98 1.93 1.88 1.85 1.82 1.77 1.72 1.67 1.64 1.61 1.57 1.54 1.5 1.46
40 2.84 2.44 2.23 2.09 2 1.93 1.87 1.83 1.79 1.76 1.71 1.66 1.61 1.57 1.54 1.51 1.47 1.42 1.38
60 2.79 2.39 2.18 2.04 1.95 1.87 1.82 1.77 1.74 1.71 1.66 1.6 1.54 1.51 1.48 1.44 1.4 1.35 1.29
120 2.75 2.35 2.13 1.99 1.9 1.82 1.77 1.72 1.68 1.65 1.6 1.55 1.48 1.45 1.41 1.37 1.32 1.26 1.19
∞ 2.71 2.3 2.08 1.94 1.85 1.77 1.72 1.67 1.63 1.6 1.55 1.49 1.42 1.38 1.34 1.3 1.24 1.17 1
1 161.4 199.5 215.7 224.6 280.2 234 236.8 288.9 240.5 241.9 243.9 245.9 248 249.1 250.1 251.1 252.2 253.3 254.3
2 18.51 19 19.16 19.25 19.3 19.33 19.35 19.37 19.38 19.4 19.41 19.43 19.45 19.45 19.46 1..47 19.48 19.49 19.5
3 10.18 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.74 8.7 8.66 8.64 8.62 8.59 8.57 8.55 8.53
4 7.71 6.94 6.59 6.89 6.28 6.16 6.09 6.04 6 5.96 5.91 5.86 5.8 5.77 5.75 5.72 5.89 5.66 5.63
5 6.61 5.79 5.41 6.19 5.05 4.95 4.88 4.82 4.77 4.74 4.68 4.62 4.58 4.53 4.5 4.46 4.43 4.4 4.36
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.1 4.06 4 3.94 3.87 3.84 3.81 3.77 3.74 3.7 3.67
7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.67 3.51 3.44 3.41 3.38 3.34 3.3 3.27 3.23
8 5.32 4.46 4.07 3.84 3.69 3.58 3.5 3.44 3.39 3.35 3.28 3.22 3.15 3.12 3.08 3.04 3.01 2.97 2.93
9 5.12 4.28 3.86 3.68 3.48 3.37 3.29 3.23 3.18 3.14 3.07 3.01 2.94 2.9 2.86 2.83 2.79 2.75 2.71
10 4.96 4.1 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.91 2.85 2.77 2.74 2.7 2.66 2.62 2.58 2.54
11 4.84 3.98 3.59 3.36 3.2 3.09 3.01 2.95 2.9 2.85 2.79 2.72 2.65 2.61 2.57 2.53 2.49 2.45 2.4
12 4.75 3.89 3.49 3.26 3.11 3 2.91 2.85 2.8 2.75 2.69 2.62 2.54 2.51 2.47 2.43 2.38 2.34 2.3
13 4.67 3.81 3.41 3.18 3.08 2.92 2.88 2.77 2.71 2.67 2.6 2.53 2.46 2.42 2.38 2.34 2.3 2.25 2.21
14 4.6 3.74 3.34 3.11 2.96 2.85 2.76 2.7 2.65 2.6 2.53 2.46 2.39 2.35 2.31 2.27 2.22 2.18 2.13
15 4.54 3.68 3.29 3.06 2.9 2.79 2.71 2.64 2.59 2.54 2.48 2.4 2.33 2.29 2.25 2.2 2.16 2.11 2.07
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.42 2.35 2.28 2.24 2.19 2.15 2.11 2.06 2.01
17 4.45 3.59 3.2 2.96 2.81 2.7 2.61 2.55 2.49 2.46 2.38 2.31 2.23 2.19 2.16 2.1 2.06 2.01 1.96
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.34 2.27 2.19 2.15 2.11 2.06 2.02 1.97 1.92
19 4.38 3.52 3.13 2.9 2.74 2.63 2.54 2.48 2.42 2.38 2.31 2.23 2.16 2.11 2.07 2.03 1.98 1.93 1.88
20 4.35 3.49 3.1 2.87 2.71 2.6 2.51 2.45 2.39 2.35 2.28 2.2 2.12 2.08 2.04 1.99 1.95 1.9 1.84
21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.25 2.18 2.1 2.05 2.01 1.96 1.92 1.87 1.81
22 4.3 3.44 3.05 2.82 2.66 2.55 2.46 2.4 2.34 2.3 2.23 2.15 2.07 2.03 1.98 1.94 1.89 1.84 1.78
23 4.28 3.42 3.03 2.8 2.64 2.53 2.44 2.37 2.32 2.27 2.2 2.13 2.05 2.01 1.96 1.91 1.86 1.81 1.76
24 4.26 3.4 3.01 2.78 2.62 2.51 2.42 2.36 2.3 2.25 2.18 2.11 2.03 1.98 1.94 1.89 1.84 1.79 1.73
25 4.24 3.39 2.99 2.76 2.6 2.49 2.4 2.34 2.28 2.24 2.16 2.09 2.01 1.96 1.92 1.87 1.82 1.77 1.71
26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 2.15 2.07 1.99 1.95 1.9 1.85 1.8 1.75 1.69
27 4.21 3.35 2.98 2.73 2.57 2.46 2.37 2.31 2.25 2.2 2.13 2.06 1.97 1.93 1.88 1.84 1.79 1.73 1.67
28 4.2 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 2.12 2.04 1.96 1.91 1.87 1.82 1.77 1.71 1.65
29 4.18 3.33 2.93 2.7 2.55 2.43 2.35 2.28 2.22 2.18 2.1 2.03 1.94 1.9 1.85 1.81 1.75 1.7 1.64
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.09 2.01 1.93 1.89 1.84 1.79 1.74 1.68 1.62
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 2 1.92 1.84 1.79 1.74 1.69 1.64 1.58 1.51
60 4 3.15 2.76 2.53 2.37 2.26 2.17 2.1 2.04 1.99 1.92 1.84 1.75 1.7 1.65 1.59 1.53 1.47 1.39
120 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 1.91 1.83 1.75 1.66 1.61 1.55 1.5 1.43 1.35 1.25
∞ 3.34 3 2.6 2.37 2.21 2.1 2.01 1.94 1.88 1.83 1.75 1.67 1.57 1.52 1.46 1.39 1.32 1.22 1
1 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.7 963.3 968.6 976.7 984.9 993.1 997.2 1001 1006 1010 1014 1018
2 38.51 39 39.17 39.25 89.3 39.33 39.36 39.37 39.39 39.4 39.41 39.43 89.45 39.46 39.46 39.47 39.48 39.49 39.5
3 17.44 16.04 15.44 15.1 14.88 14.73 14.62 14.54 14.47 14.42 14.34 14.25 14.17 14.12 14.08 14.04 13.99 13.95 13.9
4 12.22 10.65 9.98 9.6 9.36 9.2 9.07 8.98 8.9 8.84 8.75 8.66 8.56 8.51 8.46 8.41 8.36 8.31 8.26
5 10.01 8.43 7,76 7.39 7.15 6.98 6.85 6.76 6.68 6.62 6.52 6.43 6.38 6.28 6.23 6.18 6.12 6.07 6.02
6 8.81 7.26 6.6 6.23 5.99 5.82 5.7 5.6 5.52 5.46 5.37 5.27 5.17 5.12 5.07 5.01 4.96 4.9 4.85
7 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.9 4.82 4.76 4.67 4.57 4.47 4.42 4.36 4.31 4.25 4.2 4.14
8 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36 4.3 4.2 4.1 4 3.95 3.89 3.84 3.73 3.73 3.67
9 7.21 5.71 5.08 4.72 4.48 4.32 4.2 4.1 4.08 3.96 3.87 3.77 3.67 3.61 3.56 3.51 3.45 3.39 3.33
10 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78 3.72 3.62 3.52 3.42 3.37 3.31 3.26 3.29 3.14 3.08
11 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.69 3.58 3.48 3.33 3.23 3.17 3.12 3.06 3 2.94 2.88
12 6.55 5.1 4.47 4.12 3.89 3.78 3.61 3.61 3.44 3.37 3.28 3.18 3.07 3.02 2.96 2.91 2.85 2.79 2.72
13 6.41 4.97 4.35 4 3.77 3.6 3.48 3.39 3.31 3.25 3.15 3.05 2.95 2.89 2.84 2.78 2.72 2.66 2.6
14 6.3 4.86 4.24 3.89 3.66 3.5 3.38 3.29 3.21 3.15 3.05 2.95 2.84 2.79 2.73 2.67 2.61 2.55 2.49
15 6.2 4.77 4.15 3.8 3.58 3.41 3.29 3.2 3.12 3.06 2.98 2.86 2.76 2.7 2.64 2.59 2.52 2.46 2.4
16 6.12 4.69 4.08 3.73 3.5 3.34 3.22 3.12 3.05 2.99 2.89 2.79 2.68 2.63 2.57 2.51 2.45 2.38 2.32
17 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98 2.92 2.82 2.72 2.62 2.56 2.5 2.44 2.38 2.32 2.25
18 5.98 4.56 3.95 3.61 3.38 3.22 3.1 3.01 2.93 2.87 2.77 2.67 2.56 2.5 2.44 2.38 2.32 2.26 2.19
19 5.92 4.51 3.9 3.56 3.33 3.17 3.05 2.96 2.88 2.82 2.72 2.62 2.51 2.45 2.39 2.33 2.27 2.2 2.13
20 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84 2.77 2.68 2.57 2.46 2.41 2.35 2.29 2.22 2.16 2.09
21 5.83 4.42 3.82 3.48 3.25 3.09 2.97 2.87 2.8 2.73 2.64 2.53 2.42 2.37 2.31 2.25 2.18 2.11 2.04
22 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 2.7 2.6 2.5 2.39 2.33 2.27 2.21 2.14 2.08 2
23 5.75 4.35 3.75 3.41 3.18 3.02 2.9 2.81 2.73 2.67 2.57 2.47 2.36 2.3 2.24 2.18 2.11 2.04 1.97
24 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.7 2.64 2.54 2.44 2.33 2.27 2.21 2.15 2.08 2.01 1.94
25 5.69 4.29 3.59 3.35 3.13 2.97 2.85 2.75 2.68 2.61 2.51 2.41 2.3 2.24 2.18 2.12 2.05 1.98 1.91
26 5.66 4.27 3.67 3.33 3.1 2.94 2.82 2.73 2.65 2.59 2.49 2.39 2.28 2.22 2.16 2.09 2.03 1.95 1.88
27 5.63 4.24 3.65 3.31 3.08 2.92 2.8 2.71 2.63 2.57 2.47 2.36 2.25 2.19 2.13 2.07 2 1.93 1.85
28 5.61 4.22 3.63 3.29 3.06 2.9 2.78 2.68 2.61 2.55 2.45 2.34 2.23 2.17 2.11 2.05 1.98 1.91 1.83
29 5.59 4.2 3.61 3.27 3.04 2.88 2.76 2.67 2.59 2.53 2.43 2.32 2.21 2.15 2.09 2.03 1.96 1.89 1.81
30 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57 2.51 2.41 2.31 2.2 2.14 2.07 2.01 1.94 1.87 1.79
40 5.42 4.05 3.46 3.13 2.9 2.74 2.62 2.53 2.45 2.39 2.29 2.18 2.07 2.01 1.94 1.88 1.8 1.72 1.64
60 5.29 3.93 3.34 3.01 2.79 2.68 2.51 2.41 2.33 2.27 2.17 2.06 1.94 1.88 1.82 1.74 1.67 1.58 1.48
120 5.15 3.8 3.23 2.89 2.67 2.52 2.39 2.3 2.22 2.16 2.05 1.94 1.82 1.76 1.69 1.61 1.58 1.43 1.31
∞ 5.02 3.69 3.12 2.79 2.57 2.41 2.29 2.19 2.11 2.05 1.94 1.88 1.71 1.64 1.57 1.48 1.39 1.27 1
1 4052 4999.6 5403 5625 5764 5859 5928 5982 6022 6056 6106 6157 6209 6235 6261 6287 6313 6339 6366
2 98.5 99 99.17 99.25 99.3 99.33 99.36 99.37 99.39 99.4 99.42 99.43 99.45 99.46 99.47 99.47 99.48 99.49 99.5
3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23 27.05 26.87 26.69 26.6 26.59 26.41 26.32 26.22 26.13
4 21.2 18 16.69 15.98 15.52 15.21 14.98 14.8 14.66 14.55 14.37 14.2 14.02 13.93 13.84 13.75 13.65 13.56 13.46
5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 9.89 9.72 9.55 9.47 9.38 9.29 9.2 9.11 8.02
6 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.1 7.98 7.87 7.72 7.56 7.4 7.31 7.23 7.14 7.06 6.97 6.88
7 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 6.47 6.31 6.16 6.07 5.99 5.91 5.82 5.74 5.65
8 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.67 5.52 5.36 5.28 5.2 5.12 5.03 4.95 4.86
9 10.56 8.02 6.99 6.42 6.06 5.89 5.61 5.47 5.35 5.26 5.11 4.96 4.81 4.73 4.65 4.57 4.48 4.4 4.31
10 10.04 7.56 6.55 5.99 5.64 5.39 5.2 5.06 4.94 4.85 4.71 4.56 4.41 4.38 4.25 4.17 4.08 4 3.91
11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 4.4 4.25 4.1 4.02 3.94 3.86 3.78 3.69 3.6
12 9.33 6.98 5.95 5.41 5.06 4.82 4.64 4.5 4.39 4.3 4.16 4.01 3.86 3.78 3.7 3.62 3.54 3.45 3.36
13 9.07 6.7 5.74 5.21 4.86 4.62 4.44 4.3 4.19 4.1 3.98 3.82 3.66 3.59 3.51 3.43 3.34 3.25 3.17
14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.08 3.94 3.8 3.66 3.51 3.43 3.35 3.27 3.18 3.09 3
15 8.68 6.86 5.42 4.89 4.56 4.32 4.14 4 3.89 3.8 3.67 3.52 3.37 3.29 3.21 3.13 3.05 2.96 2.87
16 8.53 6.28 5.29 4.77 4.44 4.2 4.03 3.89 3.78 3.69 3.55 3.41 3.26 3.18 3.1 3.02 2.93 2.84 2.75
17 8.4 6.11 5.18 4.67 4.34 4.1 3.93 3.79 3.68 3.59 3.46 3.31 3.16 3.08 3 2.92 2.83 2.75 2.65
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.6 3.51 3.37 3.23 3.08 3 2.92 2.84 2.75 2.66 2.57
19 8.18 5.98 5.01 4.5 4.17 3.94 3.77 3.63 3.52 3.48 3.3 3.15 3 2.92 2.84 2.76 2.67 2.58 2.49
20 8.1 5.85 4.94 4.43 4.1 3.87 3.7 3.56 3.46 3.37 3.23 3.09 2.94 2.86 2.78 2.69 2.61 2.52 2.42
21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.4 3.31 3.17 3.03 2.88 2.8 2.72 2.64 2.55 2.46 2.36
22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 3.12 2.98 2.83 2.75 2.67 2.58 2.5 2.4 2.31
23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.3 3.21 3.07 2.93 2.78 2.7 2.62 2.54 2.45 2.35 2.26
24 7.82 5.61 4.72 4.22 3.9 3.67 3.5 3.36 3.26 3.17 3.03 2.89 2.74 2.66 2.58 2.49 2.4 2.31 2.21
25 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 2.99 2.85 2.7 2.62 2.54 2.45 2.38 2.27 2.17
26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 2.96 2.81 2.66 2.58 2.5 2.42 2.33 2.23 2.13
27 7.68 5.49 4.6 4.11 3.78 3.56 3.39 3.26 3.15 3.06 2.93 2.78 2.63 2.55 2.47 2.38 2.29 2.2 2.1
28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 2.9 2.75 2.6 2.52 2.44 2.35 2.26 2.17 2.06
29 7.6 5.42 4.54 4.04 3.73 3.5 3.33 3.2 3.09 3 2.87 2.73 2.57 2.49 2.41 2.33 2.23 2.14 2.03
30 7.56 5.39 4.51 4.02 3.7 3.47 3.3 3.17 3.07 2.98 2.84 2.7 2.55 2.47 2.39 2.3 2.21 2.11 2.01
40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.8 2.66 2.52 2.37 2.29 2.2 2.11 2.02 1.92 1.8
60 7.08 4.98 4.19 3.65 3.34 3.12 2.95 2.82 2.72 2.63 2.5 2.35 2.2 2.12 2.03 1.94 1.84 1.73 1.6
120 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47 2.34 2.19 2.03 1.95 1.86 1.76 1.66 1.58 1.38
∞ 6.63 4.61 3.78 3.32 3.02 2.8 2.64 2.51 2.41 2.32 2.18 2.04 1.88 1.79 1.7 1.59 1.47 1.32 1

∂1 = degrees of freedom for numerator
∂2 = degrees of freedom for denominator

4.15.1

Related Answered Questions

Question: 4.DS.16

Two different fastener tool manufacturers have submitted their tools to the Dorf fastening tool lab for testing. The tool engineers are interested in evaluating the time required to tighten the bolt on a given test bracket. Data is collected on run-down times (from snug to fully tightened) given in ...

Verified Answer:

Approach: 1.H_{0} : \sigma ^{2}_{1}=\sigma ...
Question: 4.DS.7

Art Snakeoil, the tool manufacturer’s sales representative, now wishes to introduce a new line of pulse tools to the Purchasing Department. He indicates that historically his company has determined that the mean output torque of his line of pistol grip pulse tools is x = 42.2 Newton-Meters (Nm) ...

Verified Answer:

Approach: 1. H_0: μ ≠ μ_0 (Note tha...
Question: 4.DS.17

Control charts can be utilized to keep track of manufacturing failures. Presented below are data collected over time showing fastening torque defects, evaluating both over and under-torque conditions found per month on a vehicle assembly line. Twelve months of data were obtained for the first year ...

Verified Answer:

Approach: Since there is no previous data upon whi...
Question: 4.DS.14

A consultant is asked to evaluate some bolt failures found during testing. He is informed that the yield point of a high-strength steel (HSS) bolt is known to be normally distributed with a variance of 1.6. He decides to test the hypothesis that σ² = 1.6 against the alternative that σ² ≠ 1.6. He ...

Verified Answer:

1. H_{0} :\sigma^{2}=H_{a} :\sigma^{2} ≠1.6...
Question: 4.DS.11

Dorf Motors, a vehicle manufacturer, is interested in performing a fastener integrity reliability study of their vehicles. Dorf Motors retains a consultant to compare their fastener recall data against Fota Motors fastener recall data as presented in the NHTSA website. Eight Dorf and five Fota ...

Verified Answer:

1. n_{1} = 8 = n_{D}  n_{2} = 5 = n_{F}[/la...
Question: 4.DS.13

You are asked to evaluate the statements of a manufacturer of adhesives who claims that the shelf life of his bolt thread adhesive is approximately normally distributed with a standard deviation equal to 50 weeks. A random sample of 10 of these adhesive samples was found to have a standard ...

Verified Answer:

Approach: 1. H_{a} : σ^{2} = 2500    H_{a} ...
Question: 4.DS.12

A defense contractor has submitted to their customer, samples of a vehicle model for evaluation. The defense contractor was soon informed by their customer that most of the vehicles submitted were found to have many of the critical fasteners loosen as a result of some preliminary off-road testing. ...

Verified Answer:

1. Approach: Vehicles 1 2 3 4 5 6 7 Differences (D...
Question: 4.DS.10

Two separate assembly lines in the same manufacturing plant are utilized to apply 18 Nm torque to threaded fasteners. The torque process can be assumed to be normal, with standard deviations of σ1 = 0.019 and σ2 = 0.021. Upper management and the legal office insist that both assembly lines must ...

Verified Answer:

Approach: 1. H_{0}: μ_{1} = μ_{2} H_a:  μ_{...
Question: 4.DS.9

Art Snakeoil, the tool manufacturer’s sale representative, insists that the tools he sells are more accurate than those of his competitor and he challenges the Purchasing Department to compare the fastener tools from two plants. Plant “A” where the competitor’s tools are used and Plant “B” where ...

Verified Answer:

Approach: 1. H_{0}: μ_{1} = μ_{2} 2...
Question: 4.DS.8

In an effort to overcome the noise problem presented by his company’s impact tools (recall that μ = 89 dB) the manufacturer’s sale representative Art Snakeoil now suggests replacing the old line of noisy impact tools with his new line of quieter pistol grip impulse tools. Unfortunately, he does not ...

Verified Answer:

1. H_{0}: μ = 89 2. H_{a}[/l...