(a)
Compute the differences that exist between the burning times of the four brands of flares.
(a)
Explanation of Solution
The null and alternative hypothesis can be written as follows:
SST can be calculated as follows:
SSE can be calculated as follows:
Thus, the value of SSE is 2,236.
Table-1 shows the ANOVA Table as follows:
Table-2 | ||||
Source | Degree of freedom | Sum of square | Mean square | F |
Treatments | k-1 = 3 | SST = 662.7 | 220.9 | 3.56 |
Error | n- k = 36 | SSE = 2,236 | 62.11 |
Thus, the estimated F-value is 3.56 and p-value is 0.0236. Here, there is an adequate evidence to accomplish that differences exist between the flares with respect to burning times.
(b)
Compute theLSD with Bonferroni adjustment.
(b)
Explanation of Solution
t-value can be written as follows:
LSD can be calculated as follows:
Table-2 shows the means and difference as follows:
Table-2 | ||||||
Treatment | Means | Difference | ||||
i = 1, j =2 | 61.6 | 57.3 | 4.3 | |||
i = 1, j =3 | 61.6 | 61.8 | -2 | |||
i = 1, j =4 | 61.6 | 51.8 | 9.8 | |||
i =2, j =3 | 57.3 | 61.8 | -4.5 | |||
i =2, j =4 | 57.3 | 51.8 | 5.5 | |||
i = 3, j =4 | 61.8 | 51.8 | 10 | |||
Therefore, from the above calculation, the mean of flares C and D differs.
(c)
Compute the Tukey’s method.
(c)
Explanation of Solution
Table-2 shows the means and difference as follows:
Table-2 | ||||
Treatment | Means | Difference | ||
i = 1, j =2 | 61.6 | 57.3 | 4.3 | |
i = 1, j =3 | 61.6 | 61.8 | -2 | |
i = 1, j =4 | 61.6 | 51.8 | 9.8 | |
i =2, j =3 | 57.3 | 61.8 | -4.5 | |
i =2, j =4 | 57.3 | 51.8 | 5.5 | |
i = 3, j =4 | 61.8 | 51.8 | 10 |
Therefore, from the above calculation, the mean of flares A and D, C and D differs.
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Chapter 14 Solutions
Statistics for Management and Economics (Book Only)
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