A textile company weaves a fabric on a large number of looms. It would like the looms to be homogeneous so that it obtains a fabric of uniform strength. The process engineer suspects that, in addition to the usual variation in strength within samples of fabric fronm the same loom, there may also be significant variations in strength between looms. To investigate this, she selects four looms at random and makes four strength measurements on the fabric manufactured on each loom. The data set "fabric txt" contains the loom number followed by the strength for each measurement . a. Identify the response and the factor. Is the factor fixed or random? Explain.
b. Give the cell means and treatment effect models, along with the assumptions
c. Test for a significant effect of the loom on strength. Give the hypotheses, test statistic, P-value, and conclusion. Use α .05.
d. Estimate the variance in strength measurements made in the same loom.
e. Estimate the variance in strength measurements between looms.
Data set:
1 98
1 97
1 99
1 96
2 91
2 90
2 93
2 92
3 96
3 95
3 97
3 95
4 95
4 96
4 99
4 98