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 that a random sample of police files showed that of 32 arrests last month, 24 were of males aged 15 to 34 years. Use a 1% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.
Please provide the following information:
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? Do you think the sample size is sufficiently large? Explain. Compute the value of the sample test statistic.
(c) Find the P-value of the test statistic. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.