Question

One of largest banks in the country is researching the payment method used by restaurant customers. The interest is to know if customers have changed their method of payment with respect to last year. As the statistician in charge of the analysis you survey 220 restaurants and find historical information on payment method as shown in the table below. Allow 1% of error when performing the statistical test.

Category 2016 Market Share    2017-Observed

Credit card       0.60                   110

Debit card   0.20                        50

Personal check 0.05                            20

Cash 0.15 40

Total 1                        220

1. What is the expected value for each category?

2. What is the value of the test statistic you calculated for this problem?

3. What is the value of degrees of freedom?

4.What is the critical value for the given alpha?

5. What is your decision after performing the test?

6.What is your conclusion after performing the test? Be specific and relate to the problem.

Answer 1

The hypothesis are

H0 :  Customers have not changed their method of payment with respect to last year.

H1:  Customers have changed their method of payment with respect to last year.

1. The expected frequency is given by

E = n* p

n =

O	p	E
110	0.6	220*0.6=132
50	0.2	220*0.2=44
20	0.05	220*0.05=11
40	0.15	220*0.15=33
N= 220

2. The test statistic is given by,

(O-E)^2/E

3.667

0.818

7.364

1.485

Total = 13.333

So we have test statistic =

3. df = n - 1 = numer of categories - 1 = 4-1 = 3

4. The critical value is

5. Here calculated value of > critical value of

Hence we reject null hypothesis.

6. Conclusion :  Customers have changed their method of payment with respect to last year.