Cake. The table below shows the ranking of cakes sold on a Saturday and Sunday at a bakery shop. Do these data indicate that the Saturday and Sunday sales are equitably represented at all levels of the cake sales at the bakery?

a) What is the probability that a randomly selected sale from the bakery is one made on Sunday?

b) What is the probability that a randomly selected sale from the bakery is that of a banana chocolate cake?

c) Assuming no bias in sales, how many banana chocolate cakes are going to be sold on Sunday in the bakery?

d) To see if there is evidence of differences in sale ranks attained on the two days, will you test goodness-of-fit, homogeneity, or independence?

e) State the hypotheses.

f) Test the conditions.
g) How many degrees of freedom are there?
h) Find the chi-square value and the associated P-value.
i) State your conclusion.
j) If you concluded that the distributions are not the same, analyze the differences using the standardized residuals of your calculations.

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Top selling Saturday Sunday Cheesecake 120 258 Banana chocolate 104 195 Black forest 95 142 New York cheesecake 73 132 Red bean 55 30 Mocha 29 11