Question

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 of 34 arrests last month, 24 were of 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 Z value?
What is the P Value?
Is this left or right tailed?
Is the information significant?

Answer 1

$Z-value:\;z=\frac{\frac{24}{34}-0.7}{\sqrt{\frac{0.7*(1-0.7)}{34}}}=0.07.\\ P-value:\;(from\;the \;tables)\;p=0.940.\\ It\;is\;two-tailed\;test.\\ Since\;the\;P-value\;is\;greater\;than\;0.10,\;the\;information\;is\;not\;significant.$