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:

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 ** 36.400 105
Pepperoni
32 40 34
31.447 37.807 36.747 *
All 89 107 104 300
Chi-sq = 0.43868 + *** + 0.320922+
0.260754+ 0.16028 + 0.004396 +
0.009736 + 0.12725 + 0.205302 = 1.5293
i. Define the null and alternative hypotheses of the χ
2
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.