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 5% of error when
performing the statistical test.

Category 2017 Market Share 2018-Observed

Credit card 0.50 100

Debit card 0.20 30

Personal check 0.05 20

Cash 0.25 70

Total 1 220

A. What is the expected value for each category?

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

c. What is the value of degrees of freedom?

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

e. What is your decision after performing the test?

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

Answer #1

applying chi square goodness of fit test:

relative | observed | Expected | residual | Chi square | |

category | frequency |
O_{i} |
E_{i}=total*p |
R^{2}_{i}=(O_{i}-E_{i})/√E_{i} |
R^{2}_{i}=(O_{i}-E_{i})^{2}/E_{i} |

credit card | 0.500 | 100 | 110.00 | -0.95 | 0.909 |

debit card | 0.200 | 30 | 44.00 | -2.11 | 4.455 |

personal check | 0.050 | 20 | 11.00 | 2.71 | 7.364 |

cash | 0.250 | 70 | 55.00 | 2.02 | 4.091 |

total | 1.000 | 220 | 220 | 16.818 |

A) expected value for each category is given in expected value column

B)value of the test statistic X^{2} =16.818

C)

degree of freedom =categories-1= | 3 |

D) critical value for the given alpha =7.815

E) as test statistic is higher than crtiical value we reject Ho

F)we conclude that *customers have changed their method of
payment with respect to last year*

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