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Sampling Error when Estimating a Population Proportion

Assume the following data represents a population of 50 values. Values equal to 1 indicate that a particular attribute is present, a value equal to 0 indicates the attribute is not present.
1......1......1......1......1......1......1......1......0......0
0......1......1......0......0......1......1......1......0......1
0......1......1......1......1......1......1......1......1......0
1......1......1......1......1......1......1......0......1......1
0......1......1......1......1......1......1......1......1......1

a. Compute the population proportion.
The population proportionate is the fraction of values in a population, which have a specific attribute. Population proportionate = X number of items having the attribute divided by N, the population size.

b. A random sample of 15 items produced the following numbers: 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0. Compute the sample proportion and the sampling error present in your sample.

c. What is the range of extreme sampling error for a sample of 15 taken from this population?

d. How would the range of extreme sampling error change if the sample size was set to 30? Discuss the advantages of having a larger sample size.

Solution Preview

Please see the attached Word document for solution and explanation for this exercise.

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Assume the following data represent a population of 50 values. Values equal
to 1 indicate that a particular attribute is present; a value equal to 0 indicates the attribute is not present.
1 1 1 1 1 1 1 1 0 0
0 1 1 0 0 1 1 1 0 1
0 1 1 1 1 1 1 1 1 0
1 1 1 1 1 1 1 0 1 1
0 1 1 1 1 1 1 1 1 1

a. Compute the population proportion.
The population proportion is the fraction of values in a population, which have a specific attribute. Population proportionate = X number of items having the attribute divided by N, the population size.

The attribute is present ...

Solution Summary

In this solution, questions about sampling error when estimating a population proportion are discussed within an attached Word document. All calculation details are provided along with explanations.

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