The Restaurant Critic on a Newspaper Claims That the Hamburgers $\quad$

Essay

The restaurant critic on a newspaper claims that the hamburgers one gets at the hamburger chain restaurants are all equally bad, and that people who claim to like one hamburger over others are victims of advertising. In fact, he claims that if there were no differences in appearance, then all hamburgers would be rated equally. To test the critic's assertion, ten teenagers are asked to taste hamburgers from three different fast-food chains. Each hamburger is dressed in the same way (mustard, relish, tomato and pickle) with the same type of bun. The teenagers taste each hamburger and rate it on a 9-point scale with 1 = bad and 9 = excellent. The data are listed below. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Ham burger Ratings }$
$\begin{array} { | c | c | c | c | } \hline \text { Teenager } & \text { Chain 1 } & \text { Chain 2 } & \text { Chain 3 } \\\hline 1 & 7 & 5 & 6 \\\hline 2 & 5 & 3 & 4 \\\hline 3 & 6 & 4 & 5 \\\hline 4 & 9 & 8 & 8 \\\hline 5 & 4 & 3 & 2 \\\hline 6 & 4 & 5 & 4 \\\hline 7 & 6 & 5 & 5 \\\hline 8 & 5 & 4 & 5 \\\hline 9 & 8 & 7 & 9 \\\hline 10 & 9 & 8 & 7 \\\hline\end{array}$ Can we infer at the 1% significance level that the critic is wrong?