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 33 arrests last month, 26 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 is the city different from 70%. Solve
the problem using both the traditional method and the
*P*-value method. Since the sampling distribution of
*p̂* is the normal distribution, you can use critical values
from the standard normal distribution as shown in the table of
critical values of the *z* distribution. (Round the test
statistic and the critical value to two decimal places. Round the
*P*-value to four decimal places.)

test statistic | = | |

critical value | = ± | |

P-value |
= |

State your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the true proportion of such arrests in the city differs from 70%.There is insufficient evidence at the 0.01 level to conclude that the true proportion of such arrests in the city differs from 70%.

Compare your conclusion with the conclusion obtained by using the
*P*-value method. Are they the same?

We reject the null hypothesis using the *P*-value method,
but fail to reject using the traditional method.The conclusions
obtained by using both methods are the
same. We reject the null hypothesis using
the traditional method, but fail to reject using the
*P*-value method.

Answer #1

sample success x = | 26 | |

sample size n = | 33 | |

std error se =√(p*(1-p)/n) = | 0.0798 | |

sample proportion p̂ = x/n= | 0.7879 | |

test stat z =(p̂-p)/√(p(1-p)/n)= |
1.10 |

**critical value = -/+ 2.58**

** P-value =0.2714** (from excel function
2*(1-normsdist(1.10))

There is insufficient evidence at the 0.01 level to conclude that the true proportion of such arrests in the city differs from 70%.

The conclusions obtained by using both methods are the same.

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...

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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