Answer to Question #153367 in Statistics and Probability for sara

Question

A consumer organization was concerned

about the differences between the advertised sizes

of containers and the actual amount of product. In

a preliminary study, six packages of three different

brands of margarine that are supposed to contain

500 ml were measured. The differences from

500 ml are listed here. Do these data provide

sufficient evidence to conclude that differences exist

between the three brands? Use  = .01.

Brand 1 Brand 2 Brand 3

1 2 1

3 2 2

3 4 4

0 3 2

1 0 3

0 4 4

Answer 1

To test the difference the null and alternative hypotheses are defined as follows:

H₀: μ₁ = μ₂ = μ₃

H₁: At least two means are differ

Use the following instruction set to obtain the ANOVA table using EXCEL software:

1. Type or import data intto adjecent colomns.

2. Click Data→Data Analysis →Anova:Single Factor.

3. Specify the input range of the data.

4. Click Ok.

The EXCEL out put for the given data is as shown below:

The F value calculated 1.6863 < critical value F(crit) of 3.6823. The probability to obtain this result by chance (P-value) was calculated as 0.218 or 21.8 %. So, we are able to conclude that there was not a significant difference in the average of the three brands.