RESEARCH METHODS HANDBOOK

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Contents	Introduction	Descriptive	Hypothesis	Tables	Appendix

Comparing a Population Proportion to a Sample Proportion
(Z-test)

Assumptions

Independent random sampling

Nominal level data

Large sample size

State the Hypothesis Null Hypothesis (Ho): There is no difference between the proportion of the population (P) and the proportion of the sample (p).

Alternate Hypothesis (Ha): There is a difference between the proportion of the population and the proportion of the sample.

Ha for 1-tailed test: The proportion of the sample is greater (or less) than the proportion of the population.

Set the Rejection Criteria Establish alpha and 1-tailed or 2-tailed test

Use z-distribution table to estimate critical value

At alpha .05, 2-tailed test Zcv = 1.96
At alpha .05, 1-tailed test Zcv = 1.65 Compute the Test Statistic Standard error

p = population proportion

q = 1 - p

n = sample size

Test statistic

Decide Results of Null Hypothesis There is/is not a significant difference between the proportion of one population and the proportion of another population from which the sample was obtained.

Example