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

4.0

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).

3.5

4.1

4.5

5.1

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 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 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 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.

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

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

A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −0.77 as well as the area under the curve between 0.77 and 4 are both shaded.

(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 ??

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

(v)

Interpret your conclusion in the context of the application.

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

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