Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years.Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of32arrests last month,22were of males aged 15 to 34 years. Use a 1% level of significance to test the claim that the population proportion of such arrests is the city different from 70%. Solve the problem using both the traditional method and theP-value method. Since the sampling distribution ofpis the normal distribution, you can use critical values from the standard normal distribution as shown in thetable of critical values of thezdistribution. (Round the test statistic 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 that the true proportion of such arrests in the city differs from 70%.There is insufficient evidence at the 0.01 level to conclude that the true proportion of such arrests in the city differs from 70%.

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

The conclusions obtained by using both methods are the same.We reject the null hypothesis using theP-value method, but fail to reject using the traditional method. We reject the null hypothesis using the traditional method, but fail to reject using theP-value method.