Biostatistics Final Exam

Final Examination of Biostatistics for Premedical Students Academic Year 2017 Q1. (10 Marks) Select the correct answer 1. If A and B are two independent events such that P(A)=0.8 and P(B)=0.7, then P(A∩B)= 1.0.15 11. 0.75 iii. 0.56 iv. Otherwise. 2. If A and B are any two events, where P(AB)=0.8, P(A)=0.6 and P(B)=0.2, then A and B are called i. Independent ii. Mutually Exclusive in. Dependent iv. Otherwise. 3. Suppose we have a population of size N5, then all possible sample of size n 3 with replacement is equal to 1. 15 ii. 125 ш. 35 iv. Otherwise. 4. If the probability that a man has a high blood pressure is 0.35, if 5 men are selected randomly, then the mean and variance are respectively 1. 1.25 and 0.875 ii. 1.75 and 1.1375 iii. 2.25 and 1.325 iv. Otherwise. 5. distribution has the mean and the variance are both equal 1. Normal 11. Binomial ii. Poisson 1. Otherwise. 6. The incorrect decision of rejecting the null hypothesis when in fact it is true, creates 1. Type II error ii. Level of significance i. Type I error iv. Otherwise. 7. A statistical technique to study the relationship between two variables through a statistical model is called i. Hypothesis Testing ii. Descriptive Statistics iii. Regression Analysis iv. Otherwise. 8. The formula (rule) for Pearson's correlation coefficient is given by 1 7=1- n(n-1) 11. =1- isi. Both 1 and 11 iv. Otherwise. 9. The statistical technique that used to test whether there is any difference among the means of three or more populations are called 1. Interval estimation ii. Analysis of variance iii. Descriptive Statistics iv. Otherwise. Q2 A. (5 Marks) Punctuality of patients in keeping appointment is interest to a research team. In study of patient flow through the general practitioners, it was found that the sample of 35 patient were on average 172 minutes late for appointment with standard deviation of 8 minutes. Do these data provide sufficient evidence to indicate that the population mean is greater than 14 at 5% significant level? And construct 90% confidence interval for the population mean. Solution: Ηο: μ = 14 Η₁: μ> 14 F-17.2 11=35 21.645 Zcale= -μ 17.2-14 82 135 = 2.366 Confidence interval Acceptance region 1.645 82 17.2-1.645 < μ < 17.2 + 1.645 35 82 35 At the level of significance 0.05 we can reject Ho this is means, the population mean is greater than 14 17.976 19.424 B. (5 Marks) The true population of smoker in Benghazi in unknown and we are interested in estimating it. A random sample of size 950 persons was selected from Benghazi city and was found that 611 of team are smoker. Find the point estimate for p and construct 95% confident interval about p. Q3 A. (10 Marks) A random sample of 500 college students participated in designed to evaluate the level of collage student's knowledge of a certain group of common disease. The following table shows classification of student by the major of filed and knowledge of the group disease Knowledge of disease Good Poor Total Major Field Premedical 31 91 122 Other 19 359 378 Total 50 450 500 Do these qualitative data provide sufficient to indicate that there is relationship between major field and level of knowledge of the disease? Let a=0.05. Solution: Ho: The two phenomena under study are independence H₁: The two phenomena under study are not independence (there is relationship between them) n(AD-BC) TT2T3T4 2 500(31x359-19×91) 50 x 450 x 122 x 378 Acal =42.579 3.48 At the level of significance 0.05 we can reject Ho this is means. There is relationship between the smoking habit and the infected by lung cancer B. (10 Marks) The body weight and the length from nose to tail for 5 mice was measured, the following data were obtained Find Units of lengths (x) 4 3 5 Units of weights (y) 5 8 10 6 15 7 12 1. The correlation coefficient between the variables under study x and y. 2. The estimated regression equation of y on x. 3. By using the estimated regression line, predicted value of the weight of a mouse (y) if the length is equal to 10 (x=10) Solution: Units of lengths Units of weights xy 4 5 20 16 25 3 8 24 9 64 5 10 50 25 100 6 15 90 36 225 7 12 84 49 144 25 50 268 135 558 L T= 1x - Σχ 5(268)-(25)(50) [x² - (2x)²][Σ - (Σy)²] [5(135) - (25)²][5(558)-(50)] Strong positive correlation 0.747 2 nxy-Exy 5(268)-(25)(50) b= η Σχ² - (2x) 5(135)-(25)2 1.8 a= Σy-bx (50)-(1.8) (25) 5 - 1 y=a+bx y=1+1.8x The weight of a mouse (y) if the length is equal to 10 (x=10), y=1+1.8(10)= 19 Q5 (10 Marks) A firm wishes to compare three programs for training workers to perform a certain manual task. 15 new employees are randomly assigned to the training programs, with 5 in each program. At the end of the training period, a test is conducted to see how quickly trainees can perform the task. The number of times the task is performed per minute is recorded for each trainee Program Program Program 9 10 12 12 6 14 14 9 11 11 9 13 13 10 11 59 44 61 Σ.Σχη = 164 At a = 0.05, use these data to construct an ANOVA table and conduct f-Statistic to test that there is a difference among four programs for training Solution Η μ H₁: not all u are equal (Σ) (ΣΣ) (55 44 61 (164) SSA = 34.53 N 5 15 J=1 k SST = - (ΣΣ) N 1=1 j=1 (164) SST(9+10+12+ +9+13+13+10+11)- 66.98 15 SSWSST-SSA66.93-34.53 = 32.4 Source of variation Sum of squares SSO Degree of freedom df Mean square MSA F-Test Among Groups SSA=34.53 k-1=2 MSA=17.265 6.394 Within Groups SSW=32.4 N-k=12 MSW=2.7 Total SST=66.93 N-1-14 frale 6.394 0 -3.89 0.05 Reject Ho, we can conclude that the mean differ