Question

Step 3 of 5 :

A fast-food restaurant owner believes that when a customer orders a drink, 50% will order a regular soda, 30% will order a diet soda, and 20% will order water. To test this belief, over the course of a day she tracks how many customers order each drink. During the day 119 customers order drinks, and the breakdown by type is given in the table below:

Drink	Regular Soda	Diet Soda	Water
Customers	53	45	21

Using a 0.10 level of significance, is there sufficient evidence to conclude that the restaurant owner's belief is incorrect?

Step 3: With the observed frequencies from the table above, and the expected frequencies from the previous step, use Microsoft Excel to find the p-value of the chi-squared test for goodness of fit.

Answer 1

observed frequencey, O	expected proportion	expected frequency,E	(O-E)	(O-E)²	(O-E)²/E
53	0.500	59.50	-6.50	42.25	0.710
45	0.300	35.70	9.30	86.49	2.423
21	0.200	23.80	-2.80	7.84	0.329

chi square test statistic,X² = Σ(O-E)²/E =   3.462              
                  
level of significance, α=   0.1              
Degree of freedom=k-1=   3   -   1   =   2
                  
P value =   0.177   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value >α , Do not reject Ho                  

There is not sufficient evidence to conclude that the restaurant owner's belief is incorrect