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Investor Deposits: Sample Size Calculation - Confidence Interval

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An investment firm with 10,000 clients would like to accurately forecast the average dollar amount their current customer will deposit over the coming year. They decide to telephone a random selection of 25 of their customers to ask how much they plan to deposit, and they would like to keep this sample as small as possible so the calls do not annoy too many customers. Since they will be multiplying this average by the total number of customers to get an overall forecast, they would like to accurately estimate this average deposit for all 10,000 clients error less than $4,000. Last year the average deposit for all 10,000 clients was $25,000 with a standard deviation of $30,000. Do you think a sample of 25 is enough to give them the margin of error they want? If not, how large a sample do you suggest they need to take? Justify your answer with relevant calculations.

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Solution Summary

This problem shows how to find the sample size necessary to estimate a population mean with a given acceptable margin of error and a given level of confidence.

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A concentrator with a nominal 12,000 tonne per day capacity operates 360 days per year. The grinding circuit consists of three parallel circuits. Each circuit needs to be shut down for relining at four monthly intervals. The current method of relining takes five days to complete and costs $ 30,000 in consumable supplies. A proposed alternative method is under investigation and would involve a two day shut down and cost $ 190,000 in consumable supplies.

Should the alternative method be used if the following conditions apply:

1 Milling reserve, a minimum of 9 years supply at a head grade of 1.2 %
2 Performance of the concentrator at 1.2 % head grade is 92%, with the concentrate grading at 28% of the mineral (on a dry basis) and 10% moisture.
3 The selling price is not likely to go below $ 1.50 per kg.
4 The operating costs below are applicable

General overheads fixed at $12,000 per day
Mining fixed costs $40,000 per day
Mining variable costs $2.00 per tonne milled

Milling Fixed costs $ 24,000 per day
Milling variable costs (grinding media and power) $1.00 per tonne milled.

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