A laboratory scale is known to have a standard deviation of

A laboratory scale is known to have a standard deviation of sigma = 0.006 gram in repeated weighings. Scale readings in repeated weighings are Normally distributed, with mean equal to the true weight of the specimen. Six weighings of a specimen on the scale give an average of 3.414 grams. A 95% confidence interval for the true weight is which of the following? 3.414 plusminus 0.00403 3.414 plusminus 0.02881 3.414 plusminus 0.07056 3.414 plusminus 0.01176 3.414 plusminus 0.00196 3.414 plusminus 0.00480 3.414 plusminus 0.00033

Solution

a)

Note that

E (margin of error) = z * s / sqrt(n)

Thus, as for a 95% confidence level,

z = 1.959963985

Then, if s = 0.006, n = 6,

E = 0.004800912 = 0.00480

Thus, as the confidence interval is mean +/- E,

Confidence interval = 3.414 +/- 0.00480 [answer, option F]