Question

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 36 arrests last month, 25 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%.

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: *p* = 0.7;
*H*_{1}: *p* > 0.7 *H*_{0}:
*p* = 0 .7; *H*_{1}: *p* <
0.7 *H*_{0}: *p* =
0.7; *H*_{1}: *p* ≠ 0.7
*H*_{0}: *p* ≠ 0.7; *H*_{1}:
*p* = 0.7 *H*_{0}: *p* < 0 .7;
*H*_{1}: *p* = 0.7

(b) What sampling distribution will you use?

The standard normal, since *np* < 5 and *nq*
< 5. The standard normal, since *np* > 5 and
*nq* > 5. The Student's
*t*, since *np* < 5 and *nq* < 5. The
Student's *t*, since *np* > 5 and *nq* >
5.

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

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

(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis? Are the data statistically
significant at level *α*?

At the *α* = 0.01 level, we reject the null hypothesis
and conclude the data are statistically significant. At the
*α* = 0.01 level, we reject the null hypothesis and conclude
the data are not statistically significant.
At the *α* = 0.01 level, we fail to reject the null
hypothesis and conclude the data are statistically significant. At
the *α* = 0.01 level, we fail to reject the null hypothesis
and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the
application.

There is sufficient evidence at the 0.01 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%. There is insufficient evidence at the 0.01 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.

Answer #1

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...

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...

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...

14) 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...

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...

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...

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...

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