Question

describe an experiment requiring the stat ANOVA for analysis. describe the dependent variable, the ind variable , the levels of the ind variable and be sure to use the correct types of data for each variable.

Answer 1

Suppose, there are three production lines A, B, and C in a large manufacturing company. The company produces the items with diameter of 5 inch. All three production lines produces same product. Suppose you want to check whether there is any significant difference in the average diameter of the products produced by three different lines or not. For checking this hypothesis or claim, you need to use one way analysis of variance or ANOVA F test.

The dependent variable for this experiment is diameter of product in inches.

The independent variable for this experiment is production line. The independent variable has three levels such as A, B, and C.

Suppose you randomly collected some sample data from given three production lines and data is given as below:

Line A	Line B	Line C
6.00	5.19	5.30
5.35	5.60	5.21
5.57	5.91	5.89
5.35	5.56	5.23
5.31	5.34	5.56
4.50	4.04	4.51
4.65	4.76	4.61
4.11	4.34	4.12
4.23	4.12	4.06
4.32	4.25	4.21
4.89	4.51	4.56

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: There is no significant difference in the average diameter of the products produced by three different lines.

Alternative hypothesis: H_a: There is a significant difference in the average diameter of the products produced by three different lines.

The required ANOVA table by using excel for this test is given as below:

SUMMARY
Groups	Count	Sum	Average	Variance
Line A	11	54.28	4.934545	0.385087
Line B	11	53.62	4.874545	0.447207
Line C	11	53.26	4.841818	0.388536
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	0.048655	2	0.024327	0.05978	0.942083	3.31583
Within Groups	12.20831	30	0.406944
Total	12.25696	32

The P-value is given as 0.9421 which is greater than significance level 0.05, so we do not reject the null hypothesis.

So, there is sufficient evidence to conclude that there is no significant difference in the average diameter of the products produced by three different lines.