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 of37arrests last month,22were of males aged 15 to 34 years. Use a5%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 null and alternate hypotheses.

(a) H₀:p= 0.7;H₁:p0.7

(b) H₀:p< 0 .7;H₁:p= 0.7

(c) H₀:p= 0 .7;H₁:p< 0.7

(d) H₀:p0.7;H₁:p= 0.7

(e) H₀:p= 0.7;H₁:p> 0.7

(b) What sampling distribution will you use?

(a) The standard normal, sincenp< 5 andnq< 5.

(b) The Student'st, sincenp> 5 andnq> 5.

(c) The Student'st, sincenp< 5 andnq< 5.

(d) The standard normal, sincenp> 5 andnq> 5.

(c)What is the value of the sample test statistic? (Round your answer to two decimal places.)

(d) Find theP-value of the test statistic. (Round your answer to four decimal places.) (e) 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?

(a) At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

(b) At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

(c) At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(d) At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. 2. Letxbe per capita income in thousands of dollars. Letybe the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information aboutxandy.

x	8.5	9.6	10.5	8.0	8.3	8.7
y	9.6	18.7	20.6	10.2	11.4	13.1

Complete parts (a) through (e), givenx=53.6,y=83.6,x²=483.24,y²=1271.82,xy=767.61,andr0.956.

(a)Find x, and y. Then find the equation of the least-squares liney^=a+bx. (Round your answers forandto two decimal places. Round your answers foraandbto three decimal places.)

x= ?

Y= ?

y= ____ +_____x?

(b) Suppose a small city in Oregon has a per capita income of8.2thousand dollars. What is the predicted number of M.D.s per 10,000 residents? (Round your answer to two decimal places.)