# Qm1 Assignment Unimelb

Assignment 2 Semester 1, 2013

This assignment has four questions, and is due by 5.00pm on Thursday 2 May. It is to be submitted electronically as a .pdf ﬁle using the assignment tool on the subject’s LMS page. Marks depend on your tutor being able to understand your statements and arguments, so marks may be deducted for poor presentation or unclear language. Use nothing smaller than 12 point font. If you wish to write your assignment by hand and scan the ﬁle into a .pdf format, you may, though any illegible content will not be marked. You may work in groups of up to 4 students from the same allocated tutorial. Groups should nominate one student to submit the assignment for the whole group, with each student’s name and student number included in the document. This assignment has a total of 40 marks available and may contribute up to 10% of your ﬁnal mark in this subject. Question 1 (5 marks) Recall the concept of the sampling error from the ﬁrst and second weeks of semester. In lectures in Week 6, we considered an example in which Optus was estimating the mean telephone expenditure of a household. In the context of that example, answer each of the following questions. Where calculations are required, show all your workings. (a) Suppose we know from experience that the population standard deviation is 1200, and we want a 90% conﬁdence interval for the population value of annual telephone expenditure with an error of estimation (ie the sampling error) no greater than $50. What sample size should we use? (3 marks) (b) Suppose we want a 90% conﬁdence interval for the population value of annual telephone expenditure that is no wider than $100. What sample size should we use? (1 mark) (c) Explain in words what parts (a) and (b) tell us about the relationship between sampling error and the width of a conﬁdence interval estimate. (1 mark)

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Question 2 (21 marks) You are consulting for a farmer who grows and supplies millions of...

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