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 23 32 34 cheese 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 + *** + 0.76168 + 0.260754+ 0.16028 + 0.004396 + 0.009736 + 0.12725 + 0.205302 = 1.5293 Questions 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.
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
23 32 34
cheese 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 + *** + 0.76168 +
0.260754+ 0.16028 + 0.004396 +
0.009736 + 0.12725 + 0.205302 = 1.5293
Questions
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 a reason for your answer.
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