Is the national crime rate really going down? Some sociologistssay yes! They say that the reason for the decline in crime rates inthe 1980s and 1990s is demographics. It seems that the populationis aging, and older people commit fewer crimes. According to theFBI and the Justice Department, 70% of all arrests are of malesaged 15 to 34 years.† Suppose you are a sociologist in RockSprings, Wyoming, and a random sample of police files showed thatof 31 arrests last month, 23 were of males aged 15 to 34 years. Usea 1% level of significance to test the claim that the populationproportion of such arrests is the city different from 70%. Solvethe problem using both the traditional method and theP-value method. Since the sampling distribution ofp̂ is the normal distribution, you can use critical valuesfrom the standard normal distribution as shown in the table ofcritical values of the z distribution. (Round the teststatistic and the critical value to two decimal places. Round theP-value to four decimal places.)

test statistic	=
critical value	= ±
P-value	=

State your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude thatthe true proportion of such arrests in the city differs from70%.There is insufficient evidence at the 0.01 level to concludethat the true proportion of such arrests in the city differs from70%.    

Compare your conclusion with the conclusion obtained by using theP-value method. Are they the same?

We reject the null hypothesis using the traditional method, butfail to reject using the P-value method.We reject the nullhypothesis using the P-value method, but fail to rejectusing the traditional method.    Theconclusions obtained by using both methods are the same.