Question

The manager of a coffee shop wants to know if his customers’ drink preferences have changed in the past year. He knows that last year the preferences followed the following proportions – 34% Americano, 21% Cappuccino, 14% Espresso, 11% Latte, 10% Macchiato, 10% Other. In a random sample of 450 customers, he finds that 115 ordered Americanos, 88 ordered Cappuccinos, 69 ordered Espressos, 59 ordered Lattes, 44 ordered Macchiatos, and the rest ordered something in the Other category. Run a Goodness of Fit test to determine whether or not drink preferences have changed at his coffee shop. Use a 0.05 level of significance.

	Americanos	Capp.	Espresso	Lattes	Macchiatos	Other
Observed Counts	115	88	69	59	44	75
Expected Counts	153	94.5	63	49.5	45	45

Enter the p-value - round to 5 decimal places. Make sure you put a 0 in front of the decimal.

P-value =

Answer 1

Test Statistic () is calculated as follows:

Category	Observed (O)	Expected (E)	(O - E)2/E
Americanos	115	450X0.34=153	(115-153)2/153=9.43791
Cappuccinos	88	450X0.21=94.5	(88-94.5)2/94.5=0.44709
Espressos,	69	450X0.14=63	(69-63)2/63=0.57143
Lattes,	59	450X0.11=49.5	(59-49.5)2/49.5=1.82323
Macchiatos	44	450X0.10=45	(44-45)2/45=0.02222
Other	75	450X0.10=45	(75-45)2/45 = 20
Total = =			32.302

df = 6 - 1 = 5

By Technology,

p - value = 0.00000518

             = 0.00001 (Round to 5 decimal places.)

P - value = 0.00001