Question

Is tha national crime rata really going down? Some sociolagists say ye! Thay say that the reason for tha decline in crime rates in tha 108ds and 1990s is demographics. It seams that tha population is aging, and alder people commit fawer crimes. According to the FB and the Justice Depar ment, 70% of all arrests are of males aged 15 to 34 years. Suppose you dre a su colo ist in Rock Springs wyoming and a random sample of police files showed that of 39 arrests last month, 23 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 laval of significanca? State the null and alternate hypotheses (b) What sampling distribution will you use? The standard normal, sinca np 5 and ng 3. The Student's t, since np c and ng c s O The Student's t, since no> 5 and ng5, O The standard normal, since ng5 and ng5. what is the value of the 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.

Answer 1

a)

0.01 is the level of significanc e

H0 : p =0.7 ; H1 = p not equals to 0.7

b)

The standard normal, since np > 5 and nq > 5

test statistics:

phat = 23/39 = 0.5897

z = ( phat - p)/sqrt(p*(1-p)/n)
= (0.5897 - 0.7)/sqrt(0.7*(1-0.7)/39)
= -1.50

c)

p value = 2 *(p (z < -1.50)
= 2 * 0.0664
= 0.1328

d)

At the alpha 0.01 we fail to reject the null hypothesus and conclude the data are not statistically significant

e)

There is insufficient evidence at 0.01 level