Question

The accompanying data table contains chest deceleration measurements (in g, where g is the force of gravity) from samples of small, midsize, and large cars. Shown are the technology results for analysis of variance of this data table. Assume that a researcher plans 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. Complete parts (a) and (b) below.

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

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

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

SPSS Results |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
---|---|---|---|---|---|

Between Groups |
200.857 |
2 |
100.429 |
3.288 |
0.061 |

Within Groups |
549.714 |
18 |
30.540 |
||

Total |
750.571 |
20 |

a. What characteristic of the data specifically indicates that one-way analysis of variance should be used?

A. The measurements are categorized according to the one characteristic of size.

B. There are three samples of measurements.

C. The population means are approximately normal.

D. Nothing specifically indicates that one-way analysis of variance should be used.

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?

A. The method is based on showing that the population variances are different.

B. The method is based on estimates of a common population variance

C. The method is based on showing that the population variances are similar.

D. The method is based on estimates of multiple varying population variance

Answer #1

**Answer:-**

**(a)**

What characteristic of the data specifically indicates that one-way analysis of variance should be used?

Actually,in one way analysis measurements are categorized according to the one characteristic of size.

According to the given options,the
correct answer is **option 'A'**.

**(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?

Common population variance method

According to the given options,the
correct answer is **option 'B'**.

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Midsize car
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55
57
45
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59
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39
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54
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58
42
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46
44

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