Suppose we are testing a lab scale and want to find out if its biased or not. In

Question

Suppose we are testing a lab scale and want to find out if its biased or not. In order to do this, we plain to weigh 20 gram standard weight repeatedly. For a scale of this model, the readings are known to be distributed normally with standard deviation 0.001g. To find out if the scale is unbiased, we intend to assess the mean of repeated readings.: if it is 20g, the scale has no bias; if it is different from 20g, the scale is biased. a.) the 20g standard weight has been weighed 9 times with the average result of 20.001g. Give a 98% confidence interval for the mean of repeated measurement of the 20g weight. b.) Based on (a), formulate your opinion about the scale. c.) How many measurements would we have to make to get a margin of error of at most 0.0001 with 98% confidence?

Explanation / Answer

At 98% Confidence interval the critical value is 2.33

The Confidence interval is

Mean +/- z0.01 * SD/sqrt (n )

= 20.001 +/- 2.33 * 0.001/sqrt(9)

= 20.001 +/- 0.00078

= 20.00022, 20.00178

B) As 20 doesn't lie between the confidence interval, so the mean is not 20. so the scale is biased.

C) margin of error = 0.0001

Or, z0.01 * SD/sqrt (n ) = 0.0001

Or, 2.33 * 0.001/sqrt(n) = 0.0001

Or, sqrt(n) = 2.33 * 0.001/0.0001

Or, sqrt (n) = 23.3

Or, n = 543

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