A random sample of n₁ = 10 regions in New England gave the following violent crime rates (per million population). X₁: New England Crime Rate 3.5 3.7 4.0 4.1 3.3 4.1 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 4.3 4.5 5.5 3.3 4.8 $2 3.9 = USE SALT Assume that the crime rate distribution is approximately normal in both regions. (a) Use a calculator to calculate x₁, S₁, X2, and S₂. (Round your answers to four decimal places.) x₁ = S1 = X2 1.8 4.8 2.9 3.1 (1) What is the level of significance? 0.01 3.5 2.4 3.1 3.5 5.2 2.8 (b) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use a = 0.01. State the null and alternate hypotheses. o Hỏi thì tôi hi thi H2 o Hỏi thì = khỏi Hi khi đi thi o Hỏi thì tôi hi thì t2 o Hoi thi = tôi hi thì ti (iii) Find (or estimate) the P-value. OP-value > 0.250 (ii) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O 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 ₁-2. Round your answer to three decimal places.)
A random sample of n₁ = 10 regions in New England gave the following violent crime rates (per million population). X₁: New England Crime Rate 3.5 3.7 4.0 4.1 3.3 4.1 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 4.3 4.5 5.5 3.3 4.8 $2 3.9 = USE SALT Assume that the crime rate distribution is approximately normal in both regions. (a) Use a calculator to calculate x₁, S₁, X2, and S₂. (Round your answers to four decimal places.) x₁ = S1 = X2 1.8 4.8 2.9 3.1 (1) What is the level of significance? 0.01 3.5 2.4 3.1 3.5 5.2 2.8 (b) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use a = 0.01. State the null and alternate hypotheses. o Hỏi thì tôi hi thi H2 o Hỏi thì = khỏi Hi khi đi thi o Hỏi thì tôi hi thì t2 o Hoi thi = tôi hi thì ti (iii) Find (or estimate) the P-value. OP-value > 0.250 (ii) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O 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 ₁-2. Round your answer to three decimal places.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 4AGP
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Transcribed Image Text:A random sample of n₁ 10 regions in New England gave the following violent crime rates (per million population).
X₁: New England Crime Rate
3.5 3.7 4.0 4.1 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
4.3 4.5 5.5 3.3 4.8 3.5
3.9
USE SALT
Assume that the crime rate distribution is approximately normal in both regions.
(a) Use a calculator to calculate x₁, S₁, X2, and S₂. (Round your answers to four decimal places.)
X1 =
S1 =
x2 =
S₂ =
2.4 3.1 3.5 5.2 2.8
(b) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use a = 0.01.
(1) What is the level of significance?
0.01
State the null and alternate hypotheses.
0 Ho: H1 = Hzi Hi: H1 <H2
0 Ho: H1 =Hzi H1: H1 # H2
о но на < Hzi H1: H1 = H2
0 Ho: H1 = Hzi H1: H1 > Hz
(ii) What sampling distribution will you use? What assumptions are you making?
O The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
O The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
O 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 #₁ - ₂. Round your answer to three decimal places.)
(iii) Find (or estimate) the P-value.
OP-value> 0.250
O 0.125 P-value < 0.250
Transcribed Image Text:(iii) Find (or estimate) the P-value.
OP-value> 0.250
O 0.125 < P-value < 0.250
O 0.050 < P-value < 0.125
O 0.025 P-value < 0.050
O 0.005 < P-value < 0.025
O P-value < 0.005
Sketch the sampling distribution and show the area corresponding to the P-value.
-2
0
A
A
0
-4
-2
2
2
DO
O
2
A
0
(iv) 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?
O At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
(v) Interpret your conclusion in the context of the application.
O Fail to reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.
O Fail to 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 insufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.
O 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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