Question

A sample of n=12 students were given a test to see how quickly they could solve a task, they were then given feedback and tested again. On average, students completed the task 75 seconds faster with a standard deviation of 20 seconds. Did the feedback help improve task completion in terms of how quickly the task was completed? *We're using t tests, so I'd assume a two sample t test.*

Answer 1

Solution:

Here, we have to use paired t test.

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

Null hypothesis: H₀: The feedback does not help improve task completion in terms of how quickly the task was completed.

Alternative hypothesis: H_a: The feedback help improve task completion in terms of how quickly the task was completed.

H₀: µ_d = 0 versus H_a: µ_d > 0

This is a right tailed test.

We consider difference as time before feedback minus time after feedback.

Test statistic for paired t test is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

From given data, we have

Dbar = 75

S_d = 20

n = 12

df = n – 1 = 11

α = 0.05

t = (Dbar - µ_d)/[S_d/sqrt(n)]

t = (75 – 0)/[20/sqrt(12)]

t = 12.9904

The p-value by using t-table is given as below:

P-value = 0.0000

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the feedback help improve task completion in terms of how quickly the task was completed.