The fast-food chain McGonagles have three sizes of their takeaway haggis, Large, Jumbo and Soopersize. A survey of 300 randomly selected customers at one branch choose 92 Large, 89 Jumbo and 119 Soopersize haggises.

Is there sufficient evidence to reject the hypothesis that all three sizes are equally popular? Explain your answer carefully.

$$\left[\begin{array}{ccccccccc} \text { Distribution } & t_{1} & t_{2} & t_{3} & \chi_{1}^{2} & \chi_{2}^{2} & \chi_{3}^{2} & F_{1,2} & F_{2,3} \\ \text { 95\% percentile } & 6 \cdot 31 & 2.92 & 2 \cdot 35 & 3.84 & 5.99 & 7 \cdot 82 & 18 \cdot 51 & 9.55 \end{array}\right]$$