Answered: The Braking Distance of 8 Volkswagen…

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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The Braking Distance of 8 Volkswagen GTIs and 10 Ford Focuses were tested when traveling at 60 miles per hour on dry pavement. The results are shown below. Can you conclude that there is a difference in the mean braking distances of the two types of cars? Use α=0.01. Assume the population are normally distributed and the population variances are not equal. (See attached image.)

1. State the alternative hypothesis.

a. Ha : μ1 < μ2

b. Ha : μ1 > μ2

c. Ha : μ1 ≠ μ2

2. Level of Significance.

a. α = 0.1

b. α = 0.01

c. α = 0.001

d. β = 0.01

3. Critical Value/s and Rejection Region/s

a. Tc = ±1.645

b. Tc = ±1.833

c. Tc = ±3.496

d. Tc = ±3.499

4. Decision Rule.

a. Reject the Null Hypothesis if Tc > 1.645 or Tc < -1.645

b. Reject the Null Hypothesis if Tc > 1.833 or Tc < -1.833

c. Reject the Null Hypothesis if Tc > 3.496 or Tc < -3.496

d. Reject the Null Hypothesis if Tc > 3.499 or Tc < -3.499

5. Test statistics.

a. Tc = -2.61

b. Tc = - 4.38

c. Tc = -3.5

d. Tc = 3.5

6. Decision.

a. Reject Ho and Accept Ha

b. Accept Ho and Reject Ha

x₁ = 134
$₁ = 6.9
n₁ = 8
Volkswagen GTIS
x₂ = 143
$₂=2.6
1₂ = 10
Ford Focus

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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