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

3.3

3.7

4.2

3.9

3.3

4.1

1.8

4.8

2.9

3.1

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

3.7

4.1

4.7

5.5

3.3

4.8

3.5

2.4

3.1

3.5

5.2

2.8

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.)

x1	=
s1	=
x2	=
s2	=

(ii) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use α = 0.01.
(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ₁ < μ₂; H₁: μ₁ = μ₂H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂    H₀: μ₁ = μ₂; H₁: μ₁ > μ₂H₀: μ₁ = μ₂; H₁: μ₁ < μ₂

(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 known standard deviations.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 known standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)


(c) Find (or estimate) the P-value.

P-value > 0.2500.125 < P-value < 0.250    0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005

Answer 1

x1=c(3.3,3.7,4.2,3.9,3.3,4.1,1.8,4.8,2.9,3.1 length(x1) mean(x1) sd(x1) x2=c(3.7,4.1,4.7,5.5,3.3,4.8,3.5,2.4,3.1,3.5, 5.2,2.8) length(x2) mean(x2) sd(x2) Run it (Shift+Enter) Save it Put on a wall [ + ] Show input Absolute running time: 0.33 sec, cpu time: 0.6 sec, memory peak: 30 Mb, absolute service time: 0,34 sec [1] 10 [1] 3.51 [1] 0.8319322 [1] 12 [1] 3.883333 [1] 0.9796412

Cini: lo X = 3. 51 S, -0.832 na = 12 *2= 3.88 S2 -0.98 (ii) To test Ho: 4 = 42 us Hiiui<l2 Cal level of significance = 0.01 C. Hoiuicll2 ; H: Hi<42 (b) The student's t, we assume that both population distributions are approximately normal with unknown standard devicetions. Test Statistic, X - X2 S2 na 3.51 - 3.88 10.832) 2 (0.9792 TOTT - 0.37 0.3862 t = -0.958 cc) p-value = 0.1748 (with x=0.01, df = nitn2-2) = 10+12-2 p-value > 0.25 = 20 fail to reject the null hypothesis.