Is the national crime rate really going down? Some sociologistssay yes! They say that the reason for the decline in crime rates inthe 1980s and 1990s is demographics. It seems that the populationis aging, and older people commit fewer crimes. According to theFBI and the Justice Department, 70% of all arrests are of malesaged 15 to 34 years†. Suppose you are a sociologist in RockSprings, Wyoming, and a random sample of police files showed thatof 39 arrests last month, 26 were of males aged 15 to 34 years. Usea 5% level of significance to test the claim that the populationproportion of such arrests in Rock Springs is different from70%.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 0.7;H₁: p > 0.7

H₀: p = 0.7;H₁: p ≠0.7    

H₀: p = 0 .7;H₁: p < 0.7

H₀: p ≠ 0.7;H₁: p = 0.7

H₀: p < 0 .7;H₁: p = 0.7

(b) What sampling distribution will you use?

The Student's t, since np > 5 andnq > 5.

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 andnq < 5.

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


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


Sketch the sampling distribution and show the area corresponding tothe P-value.

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis? Are the data statisticallysignificant at level α?

At the α = 0.05 level, we reject the null hypothesisand conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesisand conclude the data are not statisticallysignificant.    

At the α = 0.05 level, we fail to reject the nullhypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the nullhypothesis and conclude the data are not statisticallysignificant.

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

There is sufficient evidence at the 0.05 level to conclude thatthe true proportion of arrests of males aged 15 to 34 in RockSprings differs from 70%.

There is insufficient evidence at the 0.05 level to concludethat the true proportion of arrests of males aged 15 to 34 in RockSprings differs from 70%.