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 35 arrests last month, 27 were of males aged 15 to 34 years. Use a 10% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.
A button hyperlink to the SALT program that reads: Use SALT.
(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 and nq < 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 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.)


Sketch the sampling distribution and show the area corresponding to the P-value.
WebAssign Plot WebAssign Plot
WebAssign Plot WebAssign Plot

(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 ?
At the = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.
At the = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the = 0.10 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 0.10 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 0.10 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.

Answer 1

Answer:

a) Level of significance $\alpha = 0.01$

b) Standard normal

$p = 0.75$

$Z = 0.62$

c)  

$P = 0.5352$

d)  

$P > \alpha$

e) We fail to reject null hypothesis  

Step-by-step explanation:

Let us say

The null hypothesis H_0 is p= 0.70 which means that Probability of arresting male of age ranging between 15 to 34 years is 0.7

Alternate hypothesis H_1 is p not equal to 0.7 which means that Probability of arresting male of age ranging between 15 to 34 years is not equal to 0.7

a) For 1% level of significance $\alpha = 0.01$

b) Standard normal

$n_p > 5\\n_q >5$

$p = \frac{24}{32} = 0.75$

$Z = \frac{(0.75-0.70)}{\sqrt{\frac{(0.7*0.3)}{32} } } = 0.62$

c)  

$P = 2 * 0.2676 = 0.5352$

d)  

$P > \alpha$

e) We fail to reject null hypothesis  

Hence, there is not enough data to prove that at 1% level of significance the probability of number of male arrested between age 15-34 is  0.70