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Sample Size

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A social service agency plans to conduct a survey to determine the mean income of its clients. The director of the agency prefers that you measure the mean income very accurately, to within + or - $500 from a sample taken 2 years ago, you estimate that the standard deviation of income for this population is about $5000 your job is to figure out the necessary sample size to reduce the confidence interval to +/- $500

a. What sample size should be drawn to meet the director's requirement at the 95% level of confidence?
b. What sample size should be drawn to meet the director's requirement at the 99% level of confidence?

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Solution Summary

The solution provides step by step method for the calculation of sample size. Formula for the calculation and Interpretations of the results are also included.

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Statistics: Standard Error and Sampling Size

Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousands) last month for each client sampled.

a. Determine the regression equation.
b. Determine the estimated sales if 40 contacts are made.

Number of contacts: X
14, 12, 20, 16, 46

Sales($thousands): Y
24, 14, 28, 30, 80

Number of contacts: X
23, 48, 50, 55, 50

Sales (Thousands): Y
30, 90, 85, 120, 110

Questions:
a. Determine the standard error of estimate.
b. Suppose a large sample is selected (instead of just 10). About 95 percent of the predictions regarding sales would occur between what two values?

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