Question: From experience, the owner of an ice-cream shop has found that 60% of all sales of ice-cream cone are for one-scoop cones, 30% are for two-scoop cones, and the remaining 10% are for three-scoop cones. Recently, the shop added frozen-yogurt cones to its menu. A random sample of 250 frozen yogurt-cone sales revealed the following distribution:

Number of scoops one two three

Number of sales 154 84 12

The owner wishes to know whether the pattern of sales for frozen-yogurt cones differs from that of ice-cream cones. Let p1, p2, and p3 be the proportions of sales of one-scoop, two-scoop, and three-scoop frozen-yogurt cones, respectively. Which one of the following pairs of null and alternative hypotheses are appropriate for this test? Explain your choice and what is wrong with each of the other choices.

A. H0: The distribution of the variable “number of scoops” is the same for frozen yogurt cones as it is for ice cream cones.

Ha: The distribution of the variable “number of scoops” is different for frozen yogurt cones than it is for ice cream cones.

B. H0: The observed counts for “number of scoops” are the same as the expected counts.

Ha: At least one of the observed counts for “number of scoops” is different from the corresponding expected count.

C. H0: Ice-cream cone sales and frozen-yogurt cone sales are independent.

Ha: Ice-cream cone sales and frozen-yogurt cone sales are dependent.