Question

The mathematical scores of groups of 4 students each are shown below. Test whether the differences in score may be attributed to chance at 5% significance level?

Group 1: Student1 is 84, Student2 is 88, Student3 is 70, Student4 is 70.

Group 2: Student1 is 90, Student2 is 95, Student3 is 93, Student4 is 80.

Group 3: Student1 is 70, Student2 is 73, Student3 is 85, Student4 is 90.

Group 4: Student1 is 95, Student2 is 96, Student3 is 90, Student4 is 90.

Group 5: Student1 is 85, Student2 is 78, Student3 is 75, Student4 is 90.

Group 6: Student1 is 93, Student2 is 85, Student3 is 80, Student4 is 90.

Answer 1

Answer the ffg.

1. Identify the treatments

2. Identify the replications

3. Identify the null and alternative hypothesis-testing

4. Define the significance level

5. The appropriate test-statistic

6. Compute

7. Define the critical region

8. Conclude

1. The treatments are group numbers 1,2,3,4,5,6

2. The replications are student numbers 1,2,3,4

3. Null hypothesis: $H_0 : \mu_1=\mu_2=\mu_3=\mu_4=\mu_5=\mu_6$

Alternative hypothesis: $H_1$ : Not all means are equal.

4. The significance level α=0.05

5. The appropriate test is ANOVA (F test)

6.

7. Critical region: Af α=0.05 and degrees of freedom

$df_1= 5$ and $df_2=18$ , the critical region for this F-test is R= {f: f>2.773}

8. As fobserved = 2.648 < F-critical = 2.773

So fail to reject H₀.