RESEARCH METHODS HANDBOOK

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Contents	Introduction	Descriptive	Hypothesis	Tables	Appendix

Example: Sample Proportion to a Population

Problem: Historical data indicates that about 10% of your agency's clients believe they were given poor service. Now under new management for six months, a random sample of 150 clients found that 15% believe they were given poor service.

Pu = .10

Ps = .15

n = 110

State the Hypothesis Ho: There is no statistically significant difference between the historical proportion of clients reporting poor service and the current proportion of clients reporting poor service.

If 2-tailed test

Ha: There is a statistically significant difference between the historical proportion of clients reporting poor service and the current proportion of clients reporting poor service.

If 1-tailed test

Ha: The proportion of current clients reporting poor service is significantly greater than the historical proportion of clients reporting poor service.

Set the Rejection Criteria If 2-tailed test, Alpha .05, Zcv = 1.96

If 1-tailed test, Alpha .05, Zcv = 1.65

Compute the Test Statistic Estimate Standard Error

Test Statistic

Decide Results of Null Hypothesis If a 2-tailed test was used

Since the test statistic of 1.724 did not meet or exceed the critical value of 1.96, you must conclude there is no statistically significant difference between the historical proportion of clients reporting poor service and the current proportion of clients reporting poor service.

If a 1-tailed test was used

Since the test statistic of 1.724 exceeds the critical value of 1.65, you can conclude the proportion of current clients reporting poor service is significantly greater than the historical proportion of clients reporting poor service.