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.

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

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'.