Question

A U.S. Senate Judiciary Committee report showed the number of homicides in each state. In Indiana, Ohio, and Kentucky, the number of homicides was, respectively, , , and . Suppose a stratified random sample with the following results was taken to learn more about the victims and the cause of death.

Stratum Sample Size Shootings Beatings Urban Victims
Indiana 30 10 9 21
Ohio 45 19 12 34
Kentucky 25 7 11 15

Required:
a. Develop an approximate confidence interval for the proportion of shooting deaths in Indiana
b. Develop an estimate for the total number of shooting deaths in Ohio (to whole number).
c. Develop an approximate confidence interval for the proportion of shooting deaths in Ohio
d. Develop an approximate confidence interval for the proportion of shooting deaths across all three states.

Answer 1

Kindly check explanation

Explanation:

Proportion of shooting deaths in Indiana:

n = 30 ; x = 10

phat = x / n = 10/30 = 0.333

1 - phat = 0.667

Tcritical 0.05 at df = 29 ; = 2.045

Phat ± Tcritical * √(phat(1 -phat) / n)

0.333 ± 2.045 * √(0.333*0.667) / 30)

0.333 ± 0.1759615

(0.157 ; 0.509)

Total deaths in ohio:

(19/45) * 760

0.4222222 * 760 = 320.88888 = 321 deaths

Proportion of shooting deaths in Ohio:

n = 45 ; x = 19

phat = x / n = 19/45 = 0.422

1 - phat = 0.578

Zcritical at 95% = 1.96

Phat ± Zcritical * √(phat(1 -phat) / n)

0.422 ± 1.96 * √(0.422*0.578) / 45)

0.422 ± 0.1443012

(0.278 ; 0.566)

D.)

Proportion of shooting deaths across all states :

n = 100 ; x = 54

phat = x / n = 54/100 = 0.54

1 - phat = 0.46

Zcritical at 95% = 2.045

Phat ± Zcritical * √(phat(1 -phat) / n)

0.54 ± 1.96 * √(0.54*0.46) / 100

47) / 30)

0.54 ± 0.0976858

(0.442 ; 0.638)