Problem 10BSC

In Exercise use analysis of variance for the indicated test.

Pelvis Injury Crash Test Data Exercise 1-4 use chest deceleration data for three different size categories (small, midsize, large). The data are from a standard crash test and they are listed in Data Set 13 in Appendix B. If we use the pelvis injury measurements (g) with the same three size categories, we get the XLSTAT results shown here. Using a 0.05 significance level, test the claim that the three size categories have the same mean pelvis injury measurement. Does the size of a car appear to affect pelvis injuries?

Exercise 1

In Exercise, use the following listed chest deceleration measurements (in g, where g is the force of gravity) from samples of small, midsize, and large cars. (These values are from Data Set 13 in Appendix B.) Also shown (on the next page) are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different size categories have the same mean chest deceleration in the standard crash test.

Chest Deceleration Measurements (g) from a Standard Crash Test

Small |
44 |
39 |
37 |
54 |
39 |
44 |
42 |

Midsize |
36 |
53 |
43 |
42 |
52 |
49 |
41 |

Large |
32 |
45 |
41 |
38 |
37 |
38 |
33 |

ANOVA

a. What characteristic of the data above indicates that we should use one-way analysis of variance?

b. If the objective is to test the claim that the three size categories have the same mean chest deceleration, why is the method referred to as analysis of variance?

Exercise 2

Why Not Test Two at a Time? Refer to the sample data given in Exercise 1. If we want to test for equality of the three means, why don’t we use three separate hypothesis tests for μ1 = μ2, μ1 = μ3, and μ2 = μ3

Exercise 3

Test Statistic What is the value of the test statistic? What distribution is used with the test statistic?

Exercise 4

P-Value If we use a 0.05 significance level in analysis of variance with the sample data given in Exercise, what is the P-value? What should we conclude?

Answer:

Step 1 of 1</p>

The Hypothesis can be expressed as

H0:

H1: At least one of them is not equal.

The P-value given in the output is 0.7111

The smaller P-value is, the stronger the evidence against H0 and in favor of H1. If...