A random sample of n 1 = 10 regions in New England gave the following violent cr

Question

A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population).

x1: New England Crime Rate

Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population).

x2: Rocky Mountain Crime Rate

Assume that the crime rate distribution is approximately normal in both regions.

(i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.)

(ii) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use = 0.05.
(a) What is the level of significance?


State the null and alternate hypotheses.

H0: 1 < 2; H1: 1 = 2H0: 1 = 2; H1: 1 > 2    H0: 1 = 2; H1: 1 < 2H0: 1 = 2; H1: 1 2

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.    The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? (Test the difference 1 2. Round your answer to three decimal places.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)


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

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

(e) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.Reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.    Fail to reject the null hypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.Fail to reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.

Explanation / Answer

1.
x1=3.48
S1=0.8066
X2=3.9
S2=0.9468

2.
Given that,
mean(x)=3.48
standard deviation , s.d1=0.8066
number(n1)=10
y(mean)=3.9
standard deviation, s.d2 =0.9468
number(n2)=12
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.833
since our test is right-tailed
reject Ho, if to > 1.833
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =3.48-3.9/sqrt((0.6506/10)+(0.89643/12))
to =-1.123
| to | =1.123
critical value
the value of |t | with min (n1-1, n2-1) i.e 9 d.f is 1.833
we got |to| = 1.12345 & | t | = 1.833
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:right tail - Ha : ( p > -1.1234 ) = 0.85484
hence value of p0.05 < 0.85484,here we do not reject Ho

ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: -1.123
critical value: 1.833
decision: do not reject Ho
p-value: 0.85484

At the = 0.05 level, we fail to reject the null hypothesis
Fail to reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.

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