Sma2110:Applied Mathematics Ii Question Paper
Sma2110:Applied Mathematics Ii
Course:Bachelor Of Computer Science
Institution: Meru University Of Science And Technology question papers
Exam Year:2010
QUESTION ONE - (30 MARKS)
a) Highlight the merits of non-parametric testing procedures. (3 Marks) b) The Kenya Police theorize that cars travel faster during the evening rush hours versus the morning rush hours and there speeds were computed using radar. The data is given below; Morning: 68, 65, 80, 61, 64, 64, 63, 73, 75, 71 Evening: 70, 70, 71, 72, 72, 71, 75, 74, 81, 72, 74, 71 Use the Mann-Whitney U test to determine if there is any evidence to suggest the median speeds are different. Use ?= 0.05. (5 Marks) c) A sample of 40 grades from a state wide examination is shown below 71 67, 55, 64, 82, 66, 74, 58, 79, 61 78, 46, 84, 93, 72, 54, 78, 86, 48, 52 67, 95, 70, 43, 70, 73, 57, 64, 60, 83 73, 40, 78, 70, 64, 86, 76, 62, 95, 66 Test the hypothesis at 0.05 significance level that the median grade for all participants is i. 66 ii. 75 (5 Marks) d) A company wishes to purchase one of five different machines; A, B, C, D or E. in an experiment designed to determine whether there is a performance difference between the machines, five experienced operators each work on the machines for equal times. The data below shows the number of units produced by each machine.
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Test the hypothesis that there is no difference between the machines at ?= 0.05 supplying all the details for the Kruskasl-Wallis H test. (5 Marks) A 68 72 77 42 53 B 72 53 63 53 48 C 60 82 64 75 72 D 48 61 57 64 50 E 64 65 70 68 53 Briefly explain how the same can be done using SSPS. (3 Marks) e) In 30 tosses of a coin the following sequence of heads (H) and tails (T) is obtained. HTTHTHHTHHTTHT HTHHTHTTHTHHTHT i. Determine the number of runs. (1 Mark) ii. Test at ?= 0.05 whether the sequence is random. (3 Marks) iii. How can this be done is SPSS. (1 Mark) f) The data below shows the heights of a sample of 12 fathers and their oldest adult sons. Find the coefficient of rank correlation. (4 Marks) Height of father: 65, 63, 67, 64, 68, 62, 70, 66, 68, 67, 69, 71 Height of son: 68, 66, 68, 65, 69, 66, 68, 65, 71, 67, 68, 70
QUESTION TWO (20 MARKS)
a) The shear strength of the bond between the two propellant type is an important characteristics. The results of testing 20 randomly selected motors are shown below; Observation (i) Shear strength ????
1 2158.70 2 1678.00 3 2316.00 4 2061.30 5 2207.50 6 1708.30 7 1784.70 8 2575.10 9 2357.90 10 2256.70 11 2165.20 12 2399.55 13 1779.80 14 2336.75 15 1765.30 16 2053.50 17 2414.40 18 2200.50 19 2654.20
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20 1753.70
i. Test the hypothesis that the median shear strength is 200Psi at ?= 0.05 using the sign test. (6 Marks) ii. Compute the wilcoxon signed rank test and test the hypothesis ??0 = ?? = 200 ?????? Vs. ???? = ?? ? 200 ?????? (6 Marks) Explain how it can be done in SPSS. (4 Marks)
iii. Use the normal approximation to test that the median shear strength is 200Psi at ?= 0.05. (4 Marks)
QUESTION THREE (20 MARKS)
a) A machine working correctly cuts pieces of wire to a mean length of 10.5cm with a standard deviation of 0.15cm. sixteen samples of wire were drawn at random from a production batch a ns measured with the following results 10.4, 10.6, 10.1, 10.3, 10.2, 10.9, 10.5, 10.8, 10.6, 10.5, 10.7, 10.2, 10.7, 10.3, 10.4, 10.5 Test the hypothesis that the machine is working correctly i.e the data fits ?? = 10.5,0.15 ???? ?= 0.05 using Kolmogorov – Smirnov goodness of fit test. (7 Marks) b) An experiment consists of tossing a coin until the first head shows up. One hundred repetitions of this experiment are performed. The frequency distribution of the number of trials required for the first head is as follows
Number of trials
1 2 3 4 5 or more
Frequency 40 32 15 7 6 Can we conclude that the coin is fair? (9 Marks) c) Consider the set of ranked elements A= 4, 12, 6, 10 B = 8,7, 16, 2 omute the enall’s rank correlation coefficient. (4 Marks)
QUESTION FOUR (20 MARKS)
a) A random sample of 500 individuals was taken to investigate whether smoking and alcohol drinking habits are related.
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Heavy drinker Moderate Non-smoker Total Heavy drinker 20 62 6 88 Moderate drinker 40 8 159 207 Non-drinker 10 20 175 205 Total 70 90 340 500
Test the hypothesis that alcohol drinking and smoking habits are independent. (7 Marks) b) Two separate groups of coaches and sports writers have ranked eight international football teams as a preseason poll exercise, as follows
A B C D E F G H Coaches 3.5 2 3.5 8 6 7 1 5 Sports writer 2 3 8 7 5.5 4 1 5.5
Test the hypothesis that there is a divert association between the two polls. (10 Marks) c) Discuss the procedures involved in a Runs test. (3 Marks)
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