Tasty Pizza Ltd desires to know if the size of the pizzas order by their customers depends on the toppings chosen. Data was gathered for the last 300 customers and the results obtained using MINITAB...

Tasty Pizza Ltd desires to know if the size of the pizzas order by their customers depends on the
toppings chosen. Data was gathered for the last 300 customers and the results obtained using
MINITAB are shown below:
Exhibit 3
Expected counts are printed below observed counts
                         Small                       Medium                       Large
 All

Cheese               23                              32                              34
                        26.403                       31.743                        30.853
 89

Tuna                   34                             35                                36
                         31.150                         **                             36.400105



Pepperoni           32                             40                                34

                           31,447                      37.807                         36.747
*

All89                              107                            104                       300

Chi-sq =                0.43868 + *** + 0.76168 +
                             0.260754+ 0.16028 + 0.004396 +
                            0.009736 + 0.12725 + 0.205302 = 1.5293
i. Define the null and alternative hypotheses of the χ²
test for the above output.
ii. Find the missing values ‘*’, ‘**’, ‘***’, Showing necessary working
iii. What is the degree of freedom for this test?
iv. Estimate the p-value for this test.
v. State the conclusion for the test. Give reason for your answer.