A company wants to conduct a telephone survey of randomly selected voters to estimate the proportion of voters who favor a particular candidate in a presidential election, to within 2% error with 95% confidence. It is guessed that the proportion is 53%.

1. What is the required minimum sample size?

2. The project manager assigned to the survey is not sure about the actual proportion or about the 2% error limit. The proportion may be anywhere from 40% to 60%. Construct a table for the minimum sample size required with half-width ranging from 1% to 3% and actual proportion ranging from 40% to 60%.

3. Inspect the table produced in question 2 above. Comment on the relative sensitivity of the minimum sample size to the actual proportion and to the desired half-width.

4. At what value of the actual proportion is the required sample size the maximum?

5. The cost of polling includes a fixed cost of $425 and a variable cost of $1.20 per person sampled, thus the cost of sampling n voters is $(425 + 1.20n). Tabulate the cost for range of values as in question 2 above.

6. A competitor of the company that had announced results to within + or - 3% with 95% confidence has started to announce results to within + or - 2% with 95% confidence. The project manager wants to go one better by improving the company's estimate to be within + or - 1% with 95% confidence. What would you tell the manager?

This is a set of solutions to six problems all related to finding the ...

Solution Summary

This is a set of solutions to six problems all related to finding the minimum sample size necessary to estimate a population parameter with a given maximum allowable error and a given level of confidence.

Q1: Why does the samplesize play such an important role in reducing the standard error of the mean? What are the implications of increasing the samplesize?
Q2: Why might one be interested in determining a samplesize before a study is undertaken? How do population variability and a level of certainty affect the size of

SampleSize for Weights of Quarters The Tyco Video Game Corporation finds that it is losing income because of slugs used in video games. The machines must be adjusted to accept coins only if they fall within set limits. In order to set these limits, the mean weight of quarters in circulation must be estimated. A sample of qu

A part that connects two levels should have a distance between the two holes of 4". It has been deternined that X-bar and R-charts should be set up to determine if the process is in statistical control. The following 100 samples of samplesize four were collected. Calculate the control limits and plot the control charts.

A sample mean, sample size, and population standard deviation are given. Use the P-value approach to perform a one-mean z-test about the mean of the population from which the sample was drawn.
x bar= 78, n = 28, sigma = 11, Hnought: mu=72, Hone: mu>72 , alpha = 0.01
First find the proper z value then use this to find the

A film alliance used a random sample of 50 U.S. citizens to estimate that the typical American spent 78 hours watching videos and DVDs last year. The standard deviation of this sample was 9 hours.
How large a sample should be used to be 90 percent confident the sample mean is within 1.0 hour of the population mean? (Round yo

A partner company to American Intellectual Union (AIU), Universal Credit Inc., would like to examine the required samplesize needed to be able to estimate the mean dollars that each card holder will spend each month. It would like to be within plus or minus $50 of the true mean with a 95% confidence level. The standard deviatio

A random sample of size n is to be drawn from a population with a mean = 500 and sd = 100. What samplesize would be necessary to ensure a standard error of 25? Samplesizes are whole numbers.
This is based on the formula for the standard error of the mean.

Given the sample data below calculate the following:
a. Sample Mean - Set One: ______
b. Sample Mean - Set Two:_____
c. Sample Std. Dev. - Set One: _____
d. Sample Std. Dev. - Set Two: _____
e. SampleSize - Set One: _____
f. SampleSize - Set Two: _
g. Hypothesis Test at LOS 0.01 if Set One has a higher population aver