426 Chapter 9 Hypothesis Testing Objective 6 Distinguish between statistical significance and practical significance Statistical Significance Is Not the Same as Practical Significance When a result has a small P-value, we say that it is ‘‘statistically significant.’’ In common usage, the word significant means ‘‘important.’’ It is therefore tempting to think that statistically significant results must always be important. This is not the case. Sometimes statistically significant results do not have any practical importance. Example 9.15 illustrates the idea. EXAMPLE 9.15 Determining practical significance At a large company, employee satisfaction is measured with a standardized test for which scores range from 0 to 100. The mean score on this test was 74. The company then implemented a new policy that allowed telecommuting, so that employees could work from home. After the policy change, the mean score for a sample of employees was 76. In order to determine whether the mean score for all employees, ��, had changed after the new policy was implemented, a hypothesis test was performed of H0 : �� = 74 H1: �� ≠ 74 We performed this test in Example 9.14. The standard error of ̄x was 0.8944 and the P-value was 0.0250, so we rejected H0 at the �� = 0.05 level. We concluded that the mean satisfaction level changed after the new policy was implemented. The human resources manager now writes a report stating that the new policy resulted in a large change in employee satisfaction. Explain why the human resources manager is not interpreting the result correctly. Solution The increase in mean score was from 74 to 76. Although this is statistically significant, it is only two points out of 100. It is unlikely that this difference is large enough to matter. The lesson here is that a result can be statistically significant without being large enough to be of practical importance. How can this happen? A difference is statistically significant when it is large compared to its standard error. In the example, a difference of two points was statistically significant because the standard error of ̄x was small —only 0.8944. When the standard error is small, even a small difference can be statistically significant. SUMMARY When a result is statistically significant, we can only conclude that the true value of the parameter is different from the value specified by H0. We cannot conclude that the difference is large enough to be important. Check Your Understanding 22. A certain type of calculator battery has a mean lifetime of 100 hours and a standard deviation of �� = 10 hours. A company has developed a new battery and claims it has a longer mean life. A random sample of 1000 batteries is tested, and their sample mean lifetime is ̄x = 101 hours. A test was made of the hypotheses H0 : �� = 100 H1: �� > 100 a. Show that H0 is rejected at the �� = 0.01 level. b. The battery manufacturer says that because the evidence is strong that �� > 100, you should be willing to pay a much higher price for its battery than for the old type of battery. Do you agree? Why or why not? Do not agree Answers are on page 433.
navidi_monk_elementary_statistics_2e_ch7-9
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