SOLUTION: Quantitative Methods | My Assignment Tutor

TRIMESTER 3 2020 FINAL EXAMINATION STUDENT ID1492184STUDENT NAMEAba e Zehra Syeda SUBJECT NAME: Quantitative Methods SUBJECT CODE: MAC004 TIME ALLOWED: 2 hours PERMITTED MATERIALS: This is an Open Book exam. INSTRUCTIONS FOR STUDENTS: You do not require a separate answer booklet. Please type your responses in the space provided.Type your full name and ID at the top of this page.This examination consists of four compulsory questions. Instruction: Read the questions below carefully. Attempt all questions. A researcher claims that the diet high in Omega-3 will have a positive impact on blood Cholesterol levels only if the Cholesterol levels for obese patients have a mean of 70. A sample of 35 patients who have tried this diet have a mean Cholesterol level of 85. Is there sufficient evidence to support the researcher’s claim? (standard deviation is 20.) (15 marks) [Answer and show workings here] μ0 = 70, σ = 20, n = 35=20/sqr root (35) =3.3885-70/3.38=4.43 The following table shows the number of workers and the amount of time in minutes it takes them to harvest the wheat WorkersTime36994700560265258390931010250 Find the regression equation. (8 marks) [Answer and show workings here] No. X Y XY 1 3 699 2097 9 488601 2 4 700 2800 16 490000 3 5 602 3010 25 362404 4 6 525 3150 36 275625 5 8 390 3120 64 152100 6 9 310 2790 81 96100 7 10 250 2500 100 62500 Total 45 3476 19467 331 1927330X avg= 45/7= 6.43 Y avg= 3476/7= 496.57b= {19467 – (45)(3476)/7} / 331- (45)^2/7b= 136269-156420/ 2317-2025 b= -20151/292 b= -69.01a= Y. avg- b. X avg a= 496.57- (-69.01) (6.43) a=496.57+443.73 a= 940.30Regression equation Y= a + bx Y= 940.30 – 69.01 x (b) Find the value of the correlation coefficient. (4 marks) [Answer and show workings here] b.R= -0.99 (Strong Indirect Correlation) (c) Use the regression equation to find how long it would take seven workers to harvest the wheat. (3 marks) [Answer and show workings here] C.Y= 940.30 – 69.01 (7) Y= 457.23 minutes for seven workers to harvest the wheat The demand for a peanut butter in each of the last five months is shown below WeekDemand150262370479592 Use a three-month moving average to generate a forecast for demand in month 6. (3 marks) [Answer and show workings here] Moving Average for three months:92+79+70/3 241/3 =80.33 demand for peanut butter for 6th month Apply exponential smoothing with a smoothing constant of 0.9 to generate a forecast for demand in month 6. (9 marks) [Answer and show workings here] Time Yi Smoothed Value Ei (i=O.9) Forecast 1 50 50 N.A 2 62 Ei = a ·Yi + (1 – a)·Ei-1 (0.9)(62)+(1-0.9)(50)=60.8 50 3 70 Ei = a ·Yi + (1 – a)·Ei-1 (0.9)(70)+(1-0.9)(60.8)=69.0860.8 4 79 Ei = a ·Yi + (1 – a)·Ei-1 (0.9)(79)+(1-0.9)(69.1)=78 69.1 5 92 Ei = a ·Yi + (1 – a)·Ei-1 (0.9)(92)+(1-0.9)(78)=90.6 78 690.6 Which of these two forecasts do you prefer and why? (3 marks) [Answer and show workings here] I prefer using exponential smoothing forecast method since in this method observations that are most recent being an analysed this it is more responsive to the occurred changes that recently happened in past. Inferential and descriptive statistics both have numerous applications, however, each serves different purposes. Using practical examples of your choice outline and then discuss differences between these two methods. ( 15 marks) [Answer here] Quantitative Methods is an analysis of raw data by managers in decision making process in numerical and quantifiable form to predict useful changes and information. The purpose of this research method is to develop theories and hypothesis based on the findings. The data is presented in mathematical and statistical form.Statistics have a vital importance in research area. It plays an important in role in gathering, analysing and presenting data findings. Statistics are divided into two major classifications. Descriptive and Inferential statistics.Descriptive statistics use and analyse data collected from a specific group where researchers attempt to reach out the findings and conclusions about that specific group only that is being analysed.In ‘Inferential statistics’, researchers use and analyse sample data in order to reach the conclusion and findings about the whole population out of which sample was taken from.Descriptive statistics use Mean, Median to find the centre of data to find where your values lie most. And uses Standard deviation and/or range to find how dispersed your data is. Graph can also be used to find frequency distribution.Both descriptive and inferential statistics applied for various purposes. Descriptive statistics are used to describe and present the data such as charts, scatter diagram, graphs etc. whereas, inferential statistics are used to make predictions and forecasts using that data.For example, if you ask a sample of 50 people from your colony if they like ice cream. You can make a pie chart of answers in YES and NO. which is describing your data so it will be descriptive statistics. This research can be used predict that population of about 50% to 65% from your colony like ice cream which is inferential data.Inferential statistics are divided into two main areas, Estimation Parameters, that is predicting something of a population by finding out population mean. Hypothesis testing, answering questions using sample date. For example if a new drug is effective in treating lung disease. Inferential alos use Confidence interval to estimate the degree to which prediction could be correct.It can also be used to compare data from your samples to other samples or reasearche s from past.Descriptive can be a simple approach but inferential can provide better evidences. END OF EXAM PAPER