You buy a big bag of 50 gumballs. There are five different colours of gumball in the bag and you are curious if each of the colours were equally likely to be put in the bag or whether some colours were more likely than others.

a. If all five colours were equally likely to be put in the bag, what would be the expected number of gumballs of each colour?

b. Suppose that you open the bag of gumballs and separate them into five piles by colour. You find that you have 8 red, 6 green, 14 orange, 5 yellow and 17 blue. Determine the 22 test statistic if the null hypothesis is that the colours of the gumballs occur with equal frequency.

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