Question

Base on the information below report your measures of effect size and proportion of variability

Write a formal paragraph to interpret your results

Problem 1: Mr. V is interested in testing if student evaluations differ from his class before and after they went online. He randomly asks 7 students to rate how much they enjoyed the class on a level of 1 to 10 before and after. The following data was collected, run the appropriate computation.

Before online: 6, 4, 8, 10, 2, 7, 5

After online: 9, 10, 7, 9, 10, 8, 10

1. Null hypothesis: There is no significant difference in student evaluations before and after they go online.

Alternative hypothesis: There is a significant difference in student evaluations before and after they go online.

2. Degrees of freedom = 6. Critical value = 2.447.

Step 3: Mean: -3
μ = 0
S² = SS⁄df = 74/(7-1) = 12.33
S²_M = S²/N = 12.33/7 = 1.76
S_M = √S²_M = √1.76 = 1.33

T-value Calculation:

t = (M - μ)/S_M = (-3 - 0)/1.33 = -2.26

Step 4:

The obtained t-value is less than the critical value. We fail to reject the null hypothesis. We can conclude that student evaluations are not significantly different before and after they went online.

Answer 1

S² = SS⁄df = 74/(7-1) = 12.33

S=3.5114

effect size=(M - μ)/S = (-3 - 0)/3.5114=0.8544

The effect size=0.8544 and greater than 0.8. Hence, the effect is large and indicates that the sample mean and population mean differ by 0.8544 standard deviation.