(a) In the past, credit card customers spent $2557 on average. To investigate whether the recent change of economy has affected the spending of the credit card customers, a marketing department of a bank selects a random sample of 98 customers for a survey. Based on the survey result, it is found that the selected customers are spending $2433 on average with a standard deviation of $367. At 10% level of significance, is there any evidence to conclude that the spending of the credit card customers has decreased? The G hypothesis H0 in this test is: OX : 2433 Op, 54 2433 Op, 5 2557 O,\" 2433 0)? g 2433 O,\" 2 2433 Op, : 2557 Op, 2 2557 O}? > 2557 Op, 54 2557 O)? 74 2433 O)? 2433 O,\" 2433 OX : 2433 Op > 2433 OX 72 2433 Op : 2557 OX > 2557 OX 3 2433 Op 35 Like the design 60 Dislike the design 14 10 21 At the 0.01 level of signicance, is there evidence of a signicant difference in the feeling about the new design among the three age groups? H0: The independent. H1: The 3 independent. The 01 = [give a value between 0 and 'I correct to 4 decimal places]. The n = The chosen test statistic is: 0t : (r MW 02 = (X \"ma/m 0x2 : 2m fer/f8 0t = (X Hl/(S/x/) oz = (IIWW and the test should be 3 test. The critical value is [give a positive value correct to 4 decimal places]. o: : (X , MSW) oz : (p , WW and the test should be 0 test. The critical value is [give a positive value correct to 4 decimal places]. The decision rule is then: Reject 3 if 4) 0 Do not reject otherwise. From the given data, the expected frequencies can be calculated using the table below: and are shown in 'b Age 35 TOTAL Like the design Dislike the design TOTAL Hence, the test statistic is found to be [correct to 4 decimal places}. Consequently, 3 and there is 3 evidence that the c 3 independent at the 0.01 level of signicance. (c) What is significance level? What is the role of significance level in hypothesis testing? Significance level is the probability of committing error, i.e., the probability of Significance level is used to determine The smaller the significance level, the the evidence is needed to reject the null hypothesis