1 THD Company allocates fixed amount of money as in the table below for weekly expenditures to its six branches (17 marks) Branches Allocation Kuala Lumpur (RM) 4000 (K) Penang (P) Ipoh (I) Alor Setar (A) Johor Bahru (J) Seremban (S) 3000 2000 2000 3000 3000 (a) Compute the number of ways to group samples of size 3 [2m] (b) Construct a sampling distribution of samples of size 3 Sampl Branche e 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 s KPI KPA KPJ KPS KIA KIJ KIS KAJ KAS PIA PIJ PIS PAJ PAS PJS IAJ IAS IJS AJS SJK [6m] Total Allocation (RM) Mean 9000 9000 10000 10000 8000 9000 9000 9000 9000 7000 8000 8000 8000 8000 9000 7000 7000 8000 8000 10000 Total 3000 3000 3333.333 3333.333 2666.667 3000 3000 3000 3000 2333.333 2666.667 2666.667 2666.667 2666.667 3000 2333.333 2333.333 2666.667 2666.667 3333.333 56666.66 7 (c) Find the mean of the sampling distribution of mean [3m] (d) Find the standard deviation of the sampling distribution of mean (e) Compute the standard error of the mean [3m] [3m] Question 2 BIT Sdn. Bhd. is concerned about the petrol claim submitted by its sales personals. A random survey is done on 12 of its sales personals. The following is the result of the survey on weekly petrol claim 30 48 (10 marks) 28 40 35 28 34 46 50 32 29 38 (a) Estimate the population mean with confidence level of 95%. Assume the claim is normally distributed. [5m] (b) The company is not satisfied by the result and blamed on the sample size. Based on standard deviation obtained in (a), find the number of samples required so that for 95% confidence level will generate a margin of error of 2. [5m] Question 3 Mr. Sam is planning to invest in plantation stock market. His friend recommended three plantations stock. Mr. Sam collects random samples of monthly returns of each plantation stock and analysis them as in the following table. (15 marks) Plantation Number of Sample Standard THB Plantation Silver Hope Samples 40 46 Deviation 7.29 8.06 Plantation PLP Plantation 39 7.52 (a) Construct a 95% confidence interval of the population standard deviation of each plantation. [12m] (b) Rank the plantation stocks from less risk to the most risky investment based on the result in (a). [3m] Question 4 A telecommunication firm is introducing a new promotional pack to get more subscribers. The standard deviation of the population (subscribers) is known, 28. A random sample of 30 days sales gave a sample mean of 90 meanwhile the sample mean of similar sample sales days before the introduction of the new promotional pack is 86. The firm wants to find out if the new promotional pack boosts the sales or not. (95% confidence level) (13 marks) (a) Determine the type of test for this investigation (one tailed; left or right or two tailed test). [2m] (b) State the hypothesis for this test. [3m] (c) Determine if the new promotional pack boost the sales or not by conducting rejection region approach hypothesis test. [8m] Question 5 ATUW Motors is planning to replace the brake pad of its cars with a similar quality brake pads but cheaper. This is part of the company strategy to cut costs but wants to maintain the quality of its cars and parts. The variance of the existing brake pads life time is 29.2 months. A random sample of 24 cars gave a sample variance of 27.6 months. Determine if the new brake pads performs as better as the existing brake pads. (95% confidence level) (12 marks) Question 6 A Vedic mathematician introduces a new method to add number quickly. The mathematician plans to promote his new method to parents. He selected a group of 9 students (Group X) and trained them his method and selected randomly another group of 11 students (Group Y) who did not exposed to his method. The students were asked to solve an addition problem and the time (in seconds) taken by the students to solve the problem were recorded as the table below. Group X Group Y 18 21 20 16 17 22 25 19 29 25 16 20 20 24 20 24 27 31 18 25 (16 marks) (a) Complete the rank for Mann-Whitney test. [4m] (b) Compute the mean and standard deviation of the sum of the rank. [4m] (c) Determine if the new method is quicker to solve addition problem as claimed by the mathematician. [8m] Question 7 The Government is concerned about the rejection of housing loan for low cost housing in the country. BNM was asked to submit the average loan application received per day (per branch) and corresponding rejection rate in the year of 2015.The data is shown below. (16 marks) Number of 10 12 14 16 18 20 application Number of 2.6 2.5 2.1 1.8 1.7 1.5 rejection Find (a) The sample mean of number of loan application, x (b) The sample mean of number of loan rejected, y (c) The equation of the regression line [4m] [4m] [8m]