asty 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 ** 36.400 105   Pepperoni 32 40 34   31.447 37.807 36.747 *   Total - 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 Define the null and alternative hypotheses of the χ2 test for the above  Find the missing values ‘*’, ‘**’, ‘***’, Showing necessary working  What is the degree of freedom for this test?

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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

**

36.400

105

 

Pepperoni

32

40

34

 

31.447

37.807

36.747

*

 

Total - 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

  1. Define the null and alternative hypotheses of the χ2 test for the above 
  2. Find the missing values ‘*’, ‘**’, ‘***’, Showing necessary working 
  3. What is the degree of freedom for this test?
  4. Estimate the p-value for this 
  5. State the conclusion for the test. Give reason for your answer. 

 

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