Because of the Cost of Producing Television Shows and the Profits

question 73

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?

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Definitions:

Cyclopentane

A cyclic alkane with the formula C5H10, characterized by a ring of five carbon atoms.

Boiling Point

The temperature at which a substance changes from a liquid to a gas.

Alkanes

Hydrocarbons consisting entirely of single-bonded carbon and hydrogen atoms and are the simplest form of hydrocarbons.

Dimethylpropyl

A hydrocarbon group or moiety consisting of a propyl backbone with two methyl substituents.