question #2 Please work each of the problems completely. Include the hypothesis

Question

question #2

Please work each of the problems completely. Include the hypothesis and if the results are significant. Several studies have suggested that age has an impact on time it takes to solve tasks that have been mastered. A researcher collects data on 3 groups of people with data collected at age 20, 30, and 40. The values represent number of completed tasks. 1. 30 Years 40 Years 20 years 4 3 4 2. Analyze the 20 year old scores to the 30 year old scores using a post-hoc t-test. Is there a significant difference?

Explanation / Answer

Question 1

As you must have solved the question 1 with ANOVA analysis. That must have resulted in rejecting the null hypothesis that the the population means are different.

Question 2

Now we have to do post hoc t test analysis for the population "20 years" and "30 years"

Here as it is specified to use t test so we will use Tukey HSD test

HSD = Q *sqrt [MSW/nh]

Here for dF(error) = 9 , and k = 3 from studentized t distribution Q table

Q = 3.95

MSw= SSW/dFW = 2.25/9 = 0.25

n = 4

HSD = (3.95) * sqrt(0.25/4)= 0.9875

Mean difference = 3.75 - 1.25 = 2.5 > HSD

so there is significant difference between the two population means.

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