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Forty-five participants (15 per group) were randomly assigned to do a series of math tasks while listening to

soft-gentle music, while listening to loud-intense music, or while in silence. The means and estimated population variances for the three groups were: Soft-Gentle: M = 37, S2 = 28; Loud-Intense: M = 33, S2 = 25; Silence: M = 41, S2 = 22. 

Using the .05 significance level, is there a difference in performance on this kind of math task under these three conditions?


(a) What type of analysis should we use, and why?


(b) First, let's look at the data to prepare all the numbers we need for our hypothesis test. Identify N, Ngroups, and n as well as dfbetween, and dfwithin


Find the Grand Mean (GM)


(c) Now, let's carry out the five steps of hypothesis test.


• Step 1: State your null and alternative hypotheses. 


Step 2: The comparison distribution is an ______ distribution with ________,________ degrees of freedom


Step 3: Determine the cutoff score on this distribution (recall we are using the 0.05 significance level, Fcrit


Step 4: Calculate S2 between and S2 within. 


Using this information, find the F ratio, Fobt


Step 5: State your conclusion (i.e., whether to reject the null hypothesis) based on your results.


Please interpret this conclusion in context of what the question was asking. That is, from these findings, if you were taking a math test do you think the music in the room would matter?


Fill in the blanks: A one-way between-subjects ANoVA was performed to see whether music affects math test performance. There was/was not a significant difference in test scores across the three conditions, F( , ) = ____________, P < _________. 

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