a) A travel agency would like to know whether there is a relationship between the choice...

 

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a) A travel agency would like to know whether there is a relationship between the choice of preferred holiday and gender. A sample of 1000 tourists visiting Gold Coast is selected. The results are shown in the following table. Gender Beach Man Woman 180 125 Preferred Holiday Theme park Water sport 235 150 260 50 b) By using the chi-square test, test at 5% significance level whether the preferred holiday is independent of the gender. (8 marks) The Faculty of Accountancy, Finance and Business in TAR UC takes a random sample of 200 recent Bachelor Degree graduates and found that 20 of them are unemployed. Compute a 95% confidence interval for the proportion of all recent Bachelor Degree graduates who fail to find a job. c) (5 marks) The interest rate of a bank account is 3.6% per annum compounded every two months. (i) Calculate the effective annual rate of interest. (2 marks) (ii) If RM 10,000 is deposited into this account now, find the accrued amount after 1 year. (3 marks) BAMS1743 QUANTITATIVE METHODS Question 3 (Continued) d) The cost and the estimated net cash flows of an investment are tabulated below: Year Investment Cost (RM'000) 0 100 Net cash flow (RM'000) at year end 1 40 2 3 4 60 50 50 If the cost of capital (discount rate) is 15% per annum, calculate the net present value (NPV) for the project. Decide whether this project is worthwhile to invest and state your reason. (7 marks) [Total: 25 marks] Question 4 a) A lecturer intends to study the relationship between the barred rate and the passing rate of the students under his supervisions. The data obtained are shown in the table below. Programme RAC RBU RMK RIN RBF RFE RFI Barred rate (%), x 2.3 4.2 6.9 5 3.5 1.1 5 Passing rate (%), y 96 82 72 78 88 90 75 b) It is given that x = 28, y = 581, x = 134, y = 48677 and xy = 2234. (i) Calculate the product moment correlation coefficient and interpret the result. (5 marks) (ii) Calculate the coefficient of determination and interpret the result. (2 marks) (iii) Assuming that a linear regression model is appropriate, find the equation of the least squares regression line of y on x in the form of = a + bx. (5 marks) The following table shows the quarterly number of tickets (in thousands) sold in a theme park over the past 3 years. Year Number of tickets (in thousands) Quarter 1 Quarter 2 Quarter 3 Quarter 4 1 20 14 4 12 2 16 10 8 24 3 20 14 12 20 (i) (ii) Compute the four-quarter centred moving average trend. Calculate the average seasonal variations using the additive model. (4 marks) (6 marks) (iii) Forecast the quarterly number of tickets sold for quarter 1 in the year 5. (3 marks) [Total: 25 marks] a) A travel agency would like to know whether there is a relationship between the choice of preferred holiday and gender. A sample of 1000 tourists visiting Gold Coast is selected. The results are shown in the following table. Gender Beach Man Woman 180 125 Preferred Holiday Theme park Water sport 235 150 260 50 b) By using the chi-square test, test at 5% significance level whether the preferred holiday is independent of the gender. (8 marks) The Faculty of Accountancy, Finance and Business in TAR UC takes a random sample of 200 recent Bachelor Degree graduates and found that 20 of them are unemployed. Compute a 95% confidence interval for the proportion of all recent Bachelor Degree graduates who fail to find a job. c) (5 marks) The interest rate of a bank account is 3.6% per annum compounded every two months. (i) Calculate the effective annual rate of interest. (2 marks) (ii) If RM 10,000 is deposited into this account now, find the accrued amount after 1 year. (3 marks) BAMS1743 QUANTITATIVE METHODS Question 3 (Continued) d) The cost and the estimated net cash flows of an investment are tabulated below: Year Investment Cost (RM'000) 0 100 Net cash flow (RM'000) at year end 1 40 2 3 4 60 50 50 If the cost of capital (discount rate) is 15% per annum, calculate the net present value (NPV) for the project. Decide whether this project is worthwhile to invest and state your reason. (7 marks) [Total: 25 marks] Question 4 a) A lecturer intends to study the relationship between the barred rate and the passing rate of the students under his supervisions. The data obtained are shown in the table below. Programme RAC RBU RMK RIN RBF RFE RFI Barred rate (%), x 2.3 4.2 6.9 5 3.5 1.1 5 Passing rate (%), y 96 82 72 78 88 90 75 b) It is given that x = 28, y = 581, x = 134, y = 48677 and xy = 2234. (i) Calculate the product moment correlation coefficient and interpret the result. (5 marks) (ii) Calculate the coefficient of determination and interpret the result. (2 marks) (iii) Assuming that a linear regression model is appropriate, find the equation of the least squares regression line of y on x in the form of = a + bx. (5 marks) The following table shows the quarterly number of tickets (in thousands) sold in a theme park over the past 3 years. Year Number of tickets (in thousands) Quarter 1 Quarter 2 Quarter 3 Quarter 4 1 20 14 4 12 2 16 10 8 24 3 20 14 12 20 (i) (ii) Compute the four-quarter centred moving average trend. Calculate the average seasonal variations using the additive model. (4 marks) (6 marks) (iii) Forecast the quarterly number of tickets sold for quarter 1 in the year 5. (3 marks) [Total: 25 marks]