# Test of hypothesis for difference between means.

A study was conducted of the annual incomes of beginning probation officers in metropolitan areas of less than 100,000 population and in metropolitan areas having more than 500,000 population.

Some sample statistics:

Population less Population more

Sample statistic than 100,000 than 500,000

Sample size 45

Sample mean $21,290 $21,330

Sample standard

deviation $1,060

Test the statement that the annual incomes of beginning probation officers in areas having more than 500,000 population are significantly greater than those paid in areas of less than 100,000. Use the 5 percent level of risk.

It is suggested that a systematic approach be followed by stating the null and alternate hypotheses, the statistical test to be used, and so on.

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#### Solution Summary

Tests the hypothesis that the annual incomes of beginning probation officers in areas having more than 500,000 population are significantly greater than those paid in areas of less than 100,000.