Answered: A random sample of n1 = 10 regions in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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

3.3

3.9

4.2

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).

3.9

4.1

4.5

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.

(a)

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

x₁=s₁=x₂=s₂=

(b)

Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use ? = 0.01.

(i)

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

(ii)

What sampling distribution will you use? What assumptions are you making?

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

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

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