**Question 5 (Total of 18 marks)**

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

(b) **(2 marks)** 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) **(3 marks)** 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)** (9 marks) **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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#### Top Answer

(a) Construct and interpret a 95% confidence interval Lower bound: 179.7 Upper bound: 182.7 This means that the true... View the full answer