6. Production lines in a manufacturing plant are set to make steel ball bearings with a...

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6. Production lines in a manufacturing plant are set to make steel ball bearings with a diameter of 1 micron. Ten ball bearings were randomly selected from two production lines. The diameters of the ball bearings measured in microns were as follows: First line 1.18 1.42 0.69 0.88 1.62 1.09 1.53 1.02 1.19 Second line 1.72 1.62 1.69 0.79 1.79 0.77 1.44 1.29 1.96 0.99 1.32 (a) (10 points) Use the R script to calculate a 95% confidence interval for the difference between the mean diameters of ball bearings from the two production lines, assuming the variances of the diameters of ball bearings from the two production lines are the same. Is there a statistically significant difference at a = 0.05? (b) (8 points) Repeat (a) without assuming the variances of the diameters of ball bearings from the two production lines are the same. Compare the results. 6. Production lines in a manufacturing plant are set to make steel ball bearings with a diameter of 1 micron. Ten ball bearings were randomly selected from two production lines. The diameters of the ball bearings measured in microns were as follows: First line 1.18 1.42 0.69 0.88 1.62 1.09 1.53 1.02 1.19 Second line 1.72 1.62 1.69 0.79 1.79 0.77 1.44 1.29 1.96 0.99 1.32 (a) (10 points) Use the R script to calculate a 95% confidence interval for the difference between the mean diameters of ball bearings from the two production lines, assuming the variances of the diameters of ball bearings from the two production lines are the same. Is there a statistically significant difference at a = 0.05? (b) (8 points) Repeat (a) without assuming the variances of the diameters of ball bearings from the two production lines are the same. Compare the results.