(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? * hypothesis HO in this test is: OX = 2433 Ou # 2433 OH S 2557 OH 2433 OX - 2433 OH 2 2433 OH = 2557 OH 2 2557 OX > 2557 OH # 2557 OX # 2433 OX 2557 OH > 2433 Ou 2557 OX > 2433 OX = 2433 Of > 2433 OX # 2433 OH = 2557 OX > 2557 OX 2 2433 Ou 2557 OH S 2557 OH 2557 The a= [give a value between 0 and 1 correct to 4 decimal places]. The n = The chosen test statistic is: Ot = (r -p)/V(1-=)/(n-2) OZ = (P -)/ VT(1 -7) OZ = (X -1)/ (0/ Vn ) ox ? = [(fo - fellfe Ot = ( X -H)/ (S/ Vn ) and the test should be a * test. The critical value is [give a positive value correct to 4 decimal places]. The decision rule is then: Reject it Do not reject * otherwise. From the given data, the test statistic is found to be [correct to 4 decimal places]. Hence and there is * evidence that the spending of the credit card customers has * at the 0.10 level of significance. (b) A mobile phone company has a new design of smart phone and wants to investigate how customers of different age groups feel about the proposed new design. A market research survey is conducted and the responses are shown in the table below: Age 35 Like the design 22 29 60 Dislike the design 14 10 21 At the 0.01 level of significance, is there evidence of a significant difference in the feeling about the new design among the three age groups? HO: The * independent. H1: The independent. The a = [give a value between 0 and 1 correct to 4 decimal places]. The * n = The chosen test statistic is: Ot = (r -p)/v(1 -+2)/(n -2) Oz = (X -1)/(0/vn) Ox? = E( f. - fe )?if Of = (X -1 ) / (5 / VT ) OZ = (p - 7)/ VT(1 -7) and the test should be test. The critical value is [give a positive value correct to 4 decimal places]. The decision rule is then: Reject Do not reject * otherwise. From the given data, the expected frequencies can be calculated using and are shown in the table below: Age 35 TOTAL Like the design Dislike the design TOTAL Hence, the test statistic is found to be (correct to 4 decimal places]. Consequently, * and there is evidence that the independent at the 0.01 level of significance. (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