9. Measurements of the diameters of a random sample of 13 ball bearings made by machine X during one week showed a mean of 8.22 mm and a standard deviation of 0.38 mm. However, other measurements of the diameters ofa random sample of 11 ball bearings made by machine Y during the same week showed a mean of 7.68 mm and a standard deviation of 0.42 mm. Assuming the diameters are normally distributed with equal variance, a) Construct a 99% confidence interval for the difference in the true mean diameters of ball bearings made by the two machines. b) Based on your answer in part (a), are you 99% confident that the true mean diameters of ball bearings made by machines X and Y are not equal? Justify your answer.

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9. Measurements of the diameters of a random sample of 13 ball bearings made by machine X
during one week showed a mean of 8.22 mm and a standard deviation of 0.38 mm. However,
other measurements of the diameters of a random sample of 11 ball bearings made by machine
Y during the same week showed a mean of 7.68 mm and a standard deviation of 0.42 mm.
Assuming the diameters are normally distributed with equal variance,
a) Construct a 99% confidence interval for the difference in the true mean diameters of ball
bearings made by the two machines.
b) Based on your answer in part (a), are you 99% confident that the true mean diameters of
ball bearings made by machines X and Y are not equal? Justify your answer.
Transcribed Image Text:9. Measurements of the diameters of a random sample of 13 ball bearings made by machine X during one week showed a mean of 8.22 mm and a standard deviation of 0.38 mm. However, other measurements of the diameters of a random sample of 11 ball bearings made by machine Y during the same week showed a mean of 7.68 mm and a standard deviation of 0.42 mm. Assuming the diameters are normally distributed with equal variance, a) Construct a 99% confidence interval for the difference in the true mean diameters of ball bearings made by the two machines. b) Based on your answer in part (a), are you 99% confident that the true mean diameters of ball bearings made by machines X and Y are not equal? Justify your answer.
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