Quantitative Analysis for Managerial Applications

ASSIGNMENTS Course CodeMS 08 Course TitleQuantitative Analysis for Managerial Applications Assignment No. MS-08/TMA/SEM-I/2013 CoverageAll Blocks business line Attempt all the questions and submit this assignment on or before 30th April, 2013 to the coordinator of your study center. 1. A sum of 8550 is to be paid in 15 installments where each installment is 10 to a greater extent than the prior installment. Find the prototypical installment and the last installment. Let x = the original payment. The sequence of 15 payments is (1) x, x+10, x+20, x+30, , x+140 The sum of these 15 payments is 2) 15x + 10*(14*15/2) or (3) 15x + 1050 nowadays set (3) equal to the total sum to be made and place (4) 15x + 1050 = 8550 or (5) 15x = 7500 or (6) x = 500 The last payment in (1) is x + 140 or (7) 15th = 640 Answer The first payment is $500 and the last payment is $640. Ill leave it to you to add up the sequence of (1) to prove that our consequence is right. LOL 2. A salesman is go to be dn to sell a product in 3 out of 5 attempts. art object another salesman in 2 out of 5 attempts. Find the probability that a. No sales go forth happen b. Either of them will succeed in selling the productLet A be the event that the first salesman will sell the product and B be the event that the second salesman will sell the product. disposed (1) Probability that no sales will happen = P(A) ? P(B) (2) Probability that either of the salesman will succeed in selling the product = P(A) ? P(B) + P(A) ? P(B) 3. A hundred squash balls argon tested by dropping from a height of 100 inches and measuring the height of the bounce. A ball is fast if it rises above 32 inches. The sightly height of bounce was 30 inches and the measuring stick deviation was ? inches. What is the chance of getting a fast standard ball? T otal no. of observations N = 100 Mean,? 30inches Standard deviation, ? =3/4 inches=0. 75 inches judge x is the normal variable=32 inches 4. Explain the chi-squ be testing- (i ) as a test for independence of attributes, and (ii) as a test for goodness of fit. About the Chi-Square Test Generally speaking, the chi-square test is a statistical test use to examine differences with categorical variables. There are a number of features of the social world we characterize by means of categorical variables religion, political preference, etc. To examine hypotheses using such variables, use the chi-square test. The chi-square test is apply in deuce similar but distinct circumstances a. or estimating how closely an observed distribution matches an judge distribution well refer to this as the goodness-of-fit test b. for estimating whether devil random variables are independent. The Goodness-of-Fit Test One of the more interesting goodness-of-fit applications of the chi-square test is to examine issues of fairness and beguiler in games of chance, such as cards, dice, and roulette. Since such games usually involve wagering, there is signifi batcht incentive f or people to try to rig the games and allegations of missing cards, loaded dice, and adhesive roulette wheels are all too common.So how can the goodness-of-fit test be used to examine cheating in gambling? It is easier to describe the process through an example. Take the example of dice. Most dice used in wagering defecate six sides, with each side having a encourage of one, two, three, four, five, or six. If the die existence used is fair, then the chance of any particular number coming up is the same 1 in 6. However, if the die is loaded, then certain numbers will have a greater likeliness of appearing, while others will have a lower likelihood. One night at the Tunisian Nights Casino, far-famed gambler Jeremy Turner (a. k. a.The minute Master) is having a fantastic night at the craps table. In two hours of playing, hes racked up $30,000 in winnings and is showing no sign of stopping. Crowds are gathering around him to check his streak and The Missouri Master is telling a nyone within earshot that his good luck is due to the position that hes using the casinos lucky pair of bruiser dice, so named because one is total darkness and the other raunchy. Unbeknownst to Turner, however, a casino statistician has been quietly watching his rolls and marking down the values of each roll, noting the values of the black and blue dice separately.After 60 rolls, the statistician has become convinced that the blue die is loaded. Value on Blue DieObserved FrequencyExpected Frequency 11610 2510 3910 4710 5610 61710 Total6060 At first glance, this table would appear to be strong evidence that the blue die was, indeed, loaded. There are more 1s and 6s than expected, and fewer than the other numbers. However, its possible that such differences occurred by chance. The chi-square statistic can be used to estimate the likelihood that the values observed on the blue die occurred by chance. The key idea of the chi-square test is a comparison of observed and expected value s.How umpteen of something were expected and how many were observed in some process? In this case, we would expect 10 of each number to have appeared and we observed those values in the left column. With these sets of figures, we calculate the chi-square statistic as follows Using this formula with the values in the table above gives us a value of 13. 6. Lastly, to determine the significance level we need to know the degrees of freedom. In the case of the chi-square goodness-of-fit test, the number of degrees of freedom is equal to the number of terms used in conniving chi-square minus one.There were six terms in the chi-square for this problem therefore, the number of degrees of freedom is five. We then compare the value calculated in the formula above to a standard set of tables. The value returned from the table is 1. 8%. We interpret this as meaning that if the die was fair (or not loaded), then the chance of getting a ? 2 statistic as large or larger than the one calculated above is only 1. 8%. In other words, theres only a very slim chance that these rolls came from a fair die. The Missouri Master is in serious trouble. Testing IndependenceThe other primary use of the chi-square test is to examine whether two variables are independent or not. What does it mean to be independent, in this sense? It means that the two factors are not think. Typically in social science research, were interested in finding factors that are related education and income, occupation and prestige, age and voting behavior. In this case, the chi-square can be used to assess whether two variables are independent or not. More generally, we say that variable Y is not correlated with or independent of the variable X if more of one is not associated with more of another.If two categorical variables are correlated their values tend to move together, either in the same direction or in the opposite. Example Return to the example discussed at the introduction to chi-square, in which w e want to know whether boys or girls get into trouble more often in inculcate. Below is the table documenting the percentage of boys and girls who got into trouble in school Got in TroubleNo TroubleTotal Boys4671117 Girls3783120 Total83154237 To examine statistically whether boys got in trouble in school more often, we need to trap the question in terms of hypotheses.