# Conducting a hypothesis test for difference in means using a z-statistic

A study was conducted on the annual incomes of corporate trainers in the state of New York, in metropolitan areas of less than 100,000, and in metropolitan areas having a population of over 500,000. Some sample statistics are:

Sample Statistic Population less than 100K Population more than 500K

Sample Size 45 60

Sample Mean $31,290 $31,330

Sample SD $1,060 $1,900

Test the hypothesis that the annual income of corporate trainers in areas of more then 500,000 are significantly more than those in areas of less than 100,000. Use the 5% level of risk.

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#### Solution Preview

A study was conducted on the annual incomes of corporate trainers in the state of New York, in metropolitan areas of less than 100,000, and in metropolitan areas having a population of over 500,000. Some sample statistics are:

Sample Statistic Population less than 100K Population more than 500K

Sample Size 45 60

Sample Mean $31,290 ...

#### Solution Summary

The following outlines the process of conducting a hypothesis test to determine if there is a significant difference in means for two samples. Formulas and work are provided in a Word document.