**Math 221 – Principles of
Statistics**

**Introductory Examples on Hypothesis
Testing: Test Statistic**

A director of manufacturing believes production costs can be substantially reduced by changing to a new production method. Because of the cost of retooling and retraining, she must convince executives that the new method really does reduce costs. The current production method incurs mean costs of $2,150 per hour, for each assembly line, so she expresses her "research question" in terms of the hypotheses and .

A trial of 31 hours’ worth of production under the new method yields mean production costs of $1,940 (per hour). If the new method actually has the same mean hourly production cost as the old method, calculate the z-score of this sample mean. (Assume the standard deviation of the production costs is $495 per hour, under the new method.)

NOTE: The z-score corresponding to $1,940 is called the *
test statistic* of the hypothesis test.

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