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Because of the Cost of Producing Television Shows and the Profits

Question 123

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Because of the cost of producing television shows and the profits associated with successful shows, television network executives are keenly interested in public opinion. A network has recently developed three comedy series. The pilot of each series is shown to 10 randomly selected people, who evaluate each show on a 9-point scale where 1 = terrible and 9 = excellent. The results are shown below.  Assessments of Televion Shows  Person  Show 1  Show 2  Show 3 16472545376847785999657674458637956610778\begin{array} { | c | c | c | c | } \hline&&{ \text { Assessments of Televion Shows } } \\\hline \text { Person } & \text { Show 1 } & \text { Show 2 } & \text { Show 3 } \\\hline 1 & 6 & 4 & 7 \\\hline 2 & 5 & 4 & 5 \\\hline 3 & 7 & 6 & 8 \\\hline 4 & 7 & 7 & 8 \\\hline 5 & 9 & 9 & 9 \\\hline 6 & 5 & 7 & 6 \\\hline 7 & 4 & 4 & 5 \\\hline 8 & 6 & 3 & 7 \\\hline 9 & 5 & 6 & 6 \\\hline 10 & 7 & 7 & 8 \\\hline\end{array} Can we infer at the 5% significance level that differences exist among the show's evaluations?

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