Is the national crime rate really going down? Some sociologist say yes! They say

Question

Is the national crime rate really going down? Some sociologist 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 males 15 to 34 years. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 34 arrests last month, 22 were males aged 15 to 34 years. Use a 10% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.

What is the value of the sample test statistic?

Find the P-value of the test statistic. (Round your answer to four decimal places)

Explanation / Answer

Perform 1-sample Z test to test the claim.

Z=(Ps-Pu)/sqrt[Pu(1-Pu)/N], where Ps and Pu are sample and population proportion, N is sample size.

=(22/34-0.70)/sqrt[0.70(1-0.70/34)]

=-0.67

The p value is 0.2514.

The p value is not less than alpha=0.10, therefore, fail to reject null hypothesis. There is not sufficient sample evdience to conclude that national crime rate really going down.

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