Question

RCA has developed five alternative album covers for the new Clay Aiken cd. On cover one, Clay is surrounded by kitties. On cover two, Clay is surrounded by beautiful women in revealing swimwear. On cover three, Clay’s face has been painted to look like Peter Criss of the rock & roll band “Kiss.” On cover four, Clay is pictured playing miniature golf with his friend Ruben. On cover five, all the viewer sees is a close-up of Clay’s freshly-ironed hair. 20 subjects are shown cover 1 and asked a 5-point (1=strongly agree to 5=strongly disagree) Likert question “I want to buy this CD”, with a mean response of 4.4. 20 subjects are shown cover 2 and asked the same question, with a mean response of 2.05. 20 subjects are shown cover 3 and asked the same question with a mean response of 2.95. 20 subjects are shown cover 4 and asked the same question with a mean response of 3.20. Finally, 20 subjects are shown cover 5 and asked the same question with a mean response of 1.95. The grand mean response across all covers was 2.91. RCA researchers Tiffany Kiessling and Erica Hernandez have begun the analysis, but the computer has broken down before their analysis was complete. Take what is left and sort out the details, testing at the 0.05 level.

SSA = 79.34          SSE = 146.85

State Hypotheses:

Show work:

What is the value of the test statistic?

What is the value of the standard?

What is the result of the test?

Answer 1

Let the mean for the response to cover 1 be 1 , the mean for the response to cover 2 be 2 ,the mean for the response to cover 3 be ​​​​​​​3 , the mean for the response to cover 4 be ​​​​​​​4 , the mean for the response to cover 15be ​​​​​​​5.

The null hypothesis is given by

and the alternative hypothesis is given by

H1: at least one is different.

SSA=79.34

SSE=146.85

df of SSA is 4 and df of SSE is 19*4=76

Let the test statistic be denoted by F.

The test statistic follows F distribution with df 4,76

The value of the standard is given from the Biometrika table as

​​​​​​​

As the observed value is more than the critical value, we reject the null hypothesis at 5% level of significance and thus conclude that the means are not equal i.e. there exists significant difference between the means.

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