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Need Help from an expert. with correct answers. Thank you. All is only one question #12.

12. - POINTS BBUNDERSTAT128.3.009. MY NOTES ASK YOUR TEACHER 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 yearst. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 36 arrests last month, 26 were of males aged 15 to 34 years. Use a 5% 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. 0 Hp: P = 0.7; HT:P = 0.7 O Hp: P < 0.3; H: P = 0.7 O Hp: P = 0.3; H: P < 0.7 O Hg: = 0.7; H:p > 0.7 OHO: P = 0.7; H p 0.7 (b) What sampling distribution will you use? The standard normal, since np > 5 and ng > 5. The standard normal, since np < 5 and ng < 5. The Student's t, since np > 5 and ng > 5. The Student's t, since np < 5 and ng < 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.) Sketch the sampling distribution and show the area corresponding to the p. value.

Answer 1

a) level of signfiicance =0.05

0 Ho: P = 0.7; H: P + 0,7

b)

The standard normal, since np > 5 and ng > 5.

sample success x   =		26
sample size          n    =		36
std error   se =√(p*(1-p)/n) =		0.0764
sample proportion p̂ = x/n=		0.7222
test stat z =(p̂-p)/√(p(1-p)/n)=		0.29

c)

p value                          =

0.7718

d)

At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

e)

There is insufficient evidence at the 0.05 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%