Sampling error and sample size

Assume the following datarepresent 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.
b. A random sampleof 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 samplingerror present in your sample.
c. What is the rangeof 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.

In this solution we show how sampling error is related to sample size when estimating a population proportion.