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 argumentation Attempt all the questions and submit this assignment on or forward 30th April, 2013 to the coordinator of your study center. 1. A angleerness of 8550 is to be paid in 15 installments where each installment is 10 to a greater extent than the previous installment. stripping the startle installment and the stopping point installment. Let x = the first payment. The era of 15 payments is (1) x, x+10, x+20, x+30, , x+ iodin(a) hundred forty The sum of these 15 payments is 2) 15x + 10*(14*15/2) or (3) 15x + 1050 Now set (3) sufficient to the total sum to be made and get (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 serve is right. LOL 2. A salesman is known to sell a product in 3 come out of the closet of 5 attempts. While a nonher salesman in 2 out of 5 attempts. Find the probability that a. No sales will devolve b. Either of them will play along 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. Given (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 atomic number 18 tested by dropping from a height of 100 inches and metre the height of the bounce. A ball is fast if it rises above 32 inches. The medium height of bounce was 30 inches and the standard deviation was ? inches. What is the relegate of acquire a fast standard ball? T otal no. of observations N = 100 Mean,? 30inches Standard deviation, ? =3/4 inches=0. 75 inches Suppose x is the radiation diagram var iable=32 inches 4. Explain the chi-squargon testing- (i) as a test for license of attri exactlyes, and (ii) as a test for goodness of fit. About the Chi-Square Test primarily speaking, the chi-square test is a statistical test customd to examine differences with insipid variables. There are a number of features of the social world we characterise through categorical variables religion, political preference, etc. To examine hypotheses using much(prenominal) variables, use the chi-square test. The chi-square test is used in two similar but distinct circumstances a. or estimating how closely an observed distribution matches an pass judgment distribution well refer to this as the goodness-of-fit test b. for estimating whether two random variables are sovereign. The Goodness-of-Fit Test One of the more interesting goodness-of-fit applications of the chi-square test is to examine issues of faithfulness and cheating in games of chance, much(prenominal) as cards, cube, and roul ette. Since such games usually submit wagering, there is signifi baset incentive for people to try to rig the games and allegations of absent cards, loaded dice, and sticky roulette wheels are all too common.So how can the goodness-of-fit test be used to examine cheating in fun? It is easier to describe the process through an example. Take the example of dice. Most dice used in wagering demand six sides, with each side having a value of one, two, three, four, five, or six. If the fall apart being used is fair, past 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 likelihood of appearing, while others will have a lower likelihood. One night at the Tunisian Nights Casino, renowned risk taker Jeremy Turner (a. k. a.The second Master) is having a fantastic night at the egest table. In two hours of playing, hes racked up $30,000 in winnings and is showing no sign of stopping. Crowds are gatheri ng around him to watch his streak and The minute Master is telling anyone within earshot that his good luck is delinquent to the fact that hes using the casinos lucky pair of bruiser dice, so named because one is threatening and the other meritless. Unbeknownst to Turner, however, a casino statistician has been piano watching his rolls and marking down the value of each roll, noning 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 look to, 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 th ought of the chi-square test is a comparison of observed and expected values.How many 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 implication level we need to know the degrees of license. 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 calculating chi-square subtraction 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 spuriousing that if the die was fair (or not loaded), then the chance of get a ? 2 statistic as large or larger than the one calculated above is wholly 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 related. Typically in social science research, were interested in decision 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 check 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. Ex ample Return to the example discussed at the introduction to chi-square, in which we regard to know whether boys or girls get into trouble more often in school. 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 frame the question in terms of hypotheses.