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Inspectors have chosen twenty (20) packets of Jolly Jubes at random, and weighed them. The mean weight of the packets is 181.2 grams, with a standard deviation of 3.2 grams.

(a) Use this data to construct and interpret a 95% confidence interval for the mean weight of a packet of Jolly Jubes.

(b) Is it possible to retain 95% confidence whilst reducing the margin of error in the confidence interval? Explain briefly (you may quote a relevant formula to support your explanation)

(c) Assuming 95% confidence, and a standard deviation of 3.2 grams, what is the sample size required to estimate, to within 1 gram, the population mean weight of a packet of Jolly Jubes?

(d) Packets of Jolly Jubes are labelled as containing 180 grams of the flavourful confection. From the sample of 20 packets described above, and at the 0.05 level of significance, is there evidence that the mean weight of a packet is different from 180 grams?

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