Question

Show all work for credit (Include original formulas, hypotheses, rejection criteria, decision, and statement in context).

A comparative study of four methods for treating hyperactivity in children was performed in 16 children.  After the treatment, hyperactivity was scored on a scale of 1 to 100 where 100 is high hyperactivity.  With 99% confidence is there a statistically significant difference among hyperactivity treatments?

Treatments
1	2	3	4
42	71	41	65
35	78	44	54
40	54	27	43
39	63	39	60

10 points -Write the null and alternate hypotheses:

Null hypothesis: ________m₁=m₂=m₃=m₄______________________________________________________________________________

Alternate Hypothesis: _______differences in the means____________________________________

80 points - Fill in the chart.  Show your work for each intermediate calculation.  (Staple your work to this page.)

10 points -Are you able to reject the null hypothesis?  Show work.  Summarize your conclusion.  

Answer 1

Null hypothesis : H₀ = The treatment means are equal i.e. m₁=m₂=m₃=m₄

Alternative Hypothesis : H₀ = Atleast one pair of the treatment means are not equal i.e. m_i m_j

for i j = 1,2,3,4

Here are the calculation results :-

Conceptual Knowledge :

SS between treatments =

MS between treatments  = SS between treatments / (k-1)

SS within treatments =

MS within treatments = SS within treatments / (n-k)

F test

MS between treatments / MS within treatments ~ F(k-1, n-k)

764.2292 / 65.2292 = 11.71607 ~ F(3,12) = 2.61

Hence null hypothesis is rejected at 1% level of significance and we conclude that there is significant difference between the treatment means.

Alternatively

The f-ratio value is 11.71607. The p-value is .000705. The result is significant at p < .01. Therefore H₀ is rejected at 1% level of significance(99% confidence)