Each of a random sample of 50 five shillings coins was weighed and their masses,x grams, are summarized by

* = 474.51, 2 = 4503.8276

(i) Use an unbiased estimate of variance to calculate an approximate 90% confidence interval for the mean mass of all five shillings coins.

(ii) Estimate the size of a random of sample five shillings coins that would be required to give a 95% confidence interval whose width is half that of the interval calculated above.

(iii) It i found later that the scales were consistently under weighing by 0.05 grams.State which results of the results of (i) and (ii) should be amended and which should not.

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