Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 8–2 z Test for a Mean 421The P-values given on calculators and computers are slightly different from thosefound with Table E. This is so because z values and the values in Table E have beenrounded. Also, most calculators and computers give the exact P-value for two-tailed tests,so it should not be doubled (as it should when the area found in Table E is used).A clear distinction between the a value and the P-value should be made. The a valueis chosen by the researcher before the statistical test is conducted. The P-value is computedafter the sample mean has been found.There are two schools of thought on P-values. Some researchers do not choose an avalue but report the P-value and allow the reader to decide whether the null hypothesisshould be rejected.In this case, the following guidelines can be used, but be advised that these guidelinesare not written in stone, and some statisticians may have other opinions.Guidelines for P-ValuesIf P-value 0.01, reject the null hypothesis. The difference is highly significant.If P-value 0.01 but P-value 0.05, reject the null hypothesis. The difference is significant.If P-value 0.05 but P-value 0.10, consider the consequences of type I error beforerejecting the null hypothesis.If P-value 0.10, do not reject the null hypothesis. The difference is not significant.Others decide on the a value in advance and use the P-value to make the decision, asshown in Examples 8–6 and 8–7. A note of caution is needed here: If a researcher selectsa 0.01 and the P-value is 0.03, the researcher may decide to change the a value from0.01 to 0.05 so that the null hypothesis will be rejected. This, of course, should not bedone. If the a level is selected in advance, it should be used in making the decision.One additional note on hypothesis testing is that the researcher should distinguishbetween statistical significance and practical significance. When the null hypothesis isrejected at a specific significance level, it can be concluded that the difference is probablynot due to chance and thus is statistically significant. However, the results may not have anypractical significance. For example, suppose that a new fuel additive increases the miles per1gallon that a car can get by 4 mile for a sample of 1000 automobiles. The results may bestatistically significant at the 0.05 level, but it would hardly be worthwhile to market theproduct for such a small increase. Hence, there is no practical significance to the results. Itis up to the researcher to use common sense when interpreting the results of a statistical test.Applying the Concepts 8–2Car TheftsYou recently received a job with a company that manufactures an automobile antitheft device.To conduct an advertising campaign for the product, you need to make a claim about thenumber of automobile thefts per year. Since the population of various cities in the UnitedStates varies, you decide to use rates per 10,000 people. (The rates are based on the number ofpeople living in the cities.) Your boss said that last year the theft rate per 10,000 people was44 vehicles. You want to see if it has changed. The following are rates per 10,000 people for36 randomly selected locations in the United States.55 42 125 62 134 7339 69 23 94 73 2451 55 26 66 41 6715 53 56 91 20 7870 25 62 115 17 3658 56 33 75 20 16Source: Based on information from the National Insurance Crime Bureau.8–23