One of largest banks in the country is researching the payment method used by re
ID: 3306088 • Letter: O
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
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 the alternative hypothesis for this problem?
f. What is your decision after performing the test?
g. What is your conclusion after performing the test?
Explanation / Answer
applying chi square goodness of fit test:
a) expected frequency are calculated in above column
b) test stat =13.3333
c) degree of freedom =number of categories-1= 4-1=3
d) critical value =11.3449
e)alternative hypothesis: at least one category does not follow the proportion of method of payment with respect to last year
f) we reject null hypothesis as test stat is higher then critical value
g) we have sufficient evidence to conclude that at least one category does not follow the proportion of method of payment with respect to last year
observed Expected Chi square Type Probability O E=total*p =(O-E)^2/E credit card 0.600 110.000 132.00 3.67 debit card 0.200 50.000 44.00 0.82 personal check 0.050 20.000 11.00 7.36 cash 0.150 40.000 33.00 1.48 1 220 220 13.3333Related Questions
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