##### Question

In: Statistics and Probability

# Is the national crime rate really going down? Some sociologists say yes! They say that the...

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 of 37 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%.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

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

## Solutions

##### Expert Solution

Given that,

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 of 37 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%.

Level of significance = 0.01

(a).

The value of the sample test statistic:

The null hypothesis:

The alternative hypothesis:

The sample proportion = 24 / 37

= 0.6487

The test statistics(z):

= -0.6813

z=-0.68(Approximately)

(b).

The P-value of the test statistic:

For two tailed test,

p-value = 2 P(Z < z)

= 2 P(Z < -0.6813)

= 2 [1-P(Z < 0.6813)]

= 2 [1-0.7517]

=2 0.2483

=0.4966

The p-value=0.4966

Since p-value > 0.01 , fail to reject H0.

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