Confidence interval for the difference

Reference no: EM131015237

A production engineer in a toothpaste plant decides to study how often the toothpaste tubes are "over-filled". An "over-filled" tube "oozes" toothpaste from the tube when the end is being crimped and requires a quick slowdown of the line to remove the excess toothpaste from the crimping machine. The engineer monitors two different assembly lines for 1 hour each. On the first line, 523 tubes are filled in the hour, and the engineer records 72 over-filled tubes. On the second line, 483 tubes are filled, with 41 over-filled tubes.

(a) Test to see if the second line has a lower "over-fill" rate using a = 0.05, and explain what your results mean.

(b) Construct a 95% confidence interval for the difference in "over-fill" rates between the two assembly lines.

(c) How large a sample would be required for the test in part (a) to have a power of 0.9 for detecting a difference of 0.05?

(d) How large a sample would be required for the confidence interval in part (b) to have a margin of error of 0.05?

Reference no: EM131015237

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