Answer to Question #160546 in Statistics and Probability for Elyn

Question

The mathematical scored of 6 groups of 4 students each are shown below. Test whether the

differences in scores may be attributed to chance at 0.01 level of significance.

Student 1 2 3 4 5 6

1 87 93 75 90 80 90

2 88 95 73 96 78 85

3 70 93 85 90 75 80

4 78 79 86 80 88 87

Answer 1

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

H₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅ = μ₆

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 into 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 1.92 < critical value F(crit) of 4.24. The probability to obtain this result by chance (P-value) was calculated as 0.139 or 13.9 %. So, we are able to conclude that there was not significant difference in average between the 6 groups of students.