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.

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.

The width of a confidenceinterval estimate for a proportion will be:
A. narrower for 99% confidence than for 95% confidence
B. wider for a samplesize of 100 than for a samplesize of 50
C. narrower for 90% confidence than for 95% confidence
D. narrower when the sample proportion is 0.50 than when the sample proportion is

1, how large a samplesample should one select to be 86% confident that the sampling error is 10 or less? assume that the population standard deviation is 250.
2, a simple random sample of 500 provides 100 yes responses. compute the 94% confidenceinterval for the population proportion.

A manufacturer wishes to estimate the reliability (in months) of a certain product. An estimate of the population standard deviation from a previous sample was 12 months. If the manufacturer desires to be within 4 months of the true value with approximately 80% confidence, what should the samplesize be?

The owner of Limp Pines Resort wanted to know the average age of its clients. A random sample of 25 tourists is taken. It shows a mean age of 46 years with a standard deviation of 5 years. The width of a 98 percent CI for the true mean client age is approximately ____ years. In a samplesizecalculation for a mean, if the confid

You have been research for your statistics class on how nervous the American adults are in general, you have decided to use HINTS 2007 data set that has a scale (going from 0 to 24)measuring the psychological distress of the respondents.
a. According to HINTS 2007 data, the average psychological distress score, for this sample

Assume that a sample is drawn and z(±/2) = 1.96 and ? = 20. Answer the following questions:
(A) If the Maximum Error of Estimate is 0.02 for this sample, what would be the samplesize?
(B) Given that the sampleSize is 400 with this same z(?/2) and Ï?, what would be the Maximum Error of Estimate?
(C) What happens

A sample of size n = 14 is selected from a normal population to construct a 95% confidenceinterval estimate for a population mean. The interval was computed to be (7.82 to 9.64). Determine the sample standard deviation.

The sale manager for a hardware wholesaler finds that 229 of the previous 500 calls to the hardware store owners resulted in new product placements. Assume these 500 calls represent a random sample.
a. What is the upper confidence limit of a 95% confidenceinterval for the population proportion of new product placements?
b.

3. in an effort to estimate the annual income for new graduates, data were collected from 500 new graduates over a one -year period. assume a population standard deviation of $500.
a) if the sample mean is $15,000, what is the 95% confidenceinterval for the population mean?
b) if the sample mean is $15,000, what is the 98