Because of the Cost of Producing Television Shows and the Profits

Essay

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. $\begin{array} { | c | c | c | c | } \hline&&{ \text { Assessments of Televion Shows } } \\\hline \text { Person } & \text { Show 1 } & \text { Show 2 } & \text { Show 3 } \\\hline 1 & 6 & 4 & 7 \\\hline 2 & 5 & 4 & 5 \\\hline 3 & 7 & 6 & 8 \\\hline 4 & 7 & 7 & 8 \\\hline 5 & 9 & 9 & 9 \\\hline 6 & 5 & 7 & 6 \\\hline 7 & 4 & 4 & 5 \\\hline 8 & 6 & 3 & 7 \\\hline 9 & 5 & 6 & 6 \\\hline 10 & 7 & 7 & 8 \\\hline\end{array}$ Can we infer at the 5% significance level that differences exist among the show's evaluations?