QUESTION 1 Consider the following iron experimental data (please note four experiments were conducted on Product A and t

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: Question 1 Consider The Following Iron Experimental Data Please Note Four Experiments Were Conducted On Product A And T 1 (130.49 KiB) Viewed 25 times

: Question 1 Consider The Following Iron Experimental Data Please Note Four Experiments Were Conducted On Product A And T 2 (154.02 KiB) Viewed 25 times

QUESTION 1 Consider the following iron experimental data (please note four experiments were conducted on Product A and three on Product B): Product A iron levels are in ppm 30 32 34 Product B iron levels are in ppm 30 35 40 29 a) Is there evidence to suggest that iron levels are significantly different in the two products? (50 Marks) b) Is there evidence to suggest that the variability in the products' iron levels is significantly different? (50 Marks) QUESTION 2 a) A drug was tested on a group of sixty-five patients. Thirty out of the sixty-five patients respond to the drug. Construct a 95% confidence interval for the effectiveness of the drug based on the study data. (20 Marks) b) Formally establish if these results agree with another study conducted with the same drug involving eighty patients in which sixty patients respond to the same drug (40 Marks) c) Let p stands for the percentage who response to the drug. How many individuals must be involved in a study to ensure irrespective of what value p takes its corresponding confidence interval is approximately of size [p - 6, p +6]. (40 Marks) QUESTION 3 a) Explain with examples the following terms: i) Complete Randomisation (10 Marks) ii) Unbalanced Block Design (20 Marks) iii) Latin Squares (20 Marks) b) The number of spots on the surface of an apple can be described by a Poisson Model with u = 1.7. Calculate the following: i) P(1<x<3) (20 Marks) ii) P(X>2) (30 Marks) =

QUESTION 1 Consider the following copper experimental data (please note four experiments were conducted A and two on Product B): Product A Product B copper levels are in ppm copper levels are in ppm 60 56 62 58 63 64 (50 Marks) a) is there evidence to suggest that copper levels are significantly different in the two products? b) Is there evidence to suggest that the variability in the products' copper levels is significantly (50 Marks) different? QUESTION 2 Assuming that the iron levels in a solution was normally distributed with mean 23 mg/L and has a standard deviation of 3 mg/L. Let x denote the amount of iron in mg/L in this solution then x - N(23, 32). Calculate the following: (20 Marks) a) P(x< 26) b) P(x > 28.61 ) (20 Marks) c) P(x > 19.31 ) (20 Marks) d) P( 18.59 <x<28.28 ) - (20 Marks) e) Construct a symmetric range around the mean of x such that 95% of readings taken of this solution will have iron levels in this range. (20 Marks) QUESTION 3 a) A drug was tested on a group of fifty-five patients. Thirty out of the fifty-five patients respond to the drug. Construct a 95% confidence interval for the effectiveness of the drug based on the study data (20 Marks) b) Formally establish if these results agree with another study conducted with the same drug involving seventy patients in which forty patients respond to the same drug. (40 Marks) c) Let p stands for the percentage who response to the drug. How many individuals must be involved in a study to ensure irrespective of what value p takes its corresponding confidence interval is approximately of size [p - 2.5, p +2.5]. (40 Marks) QUESTION 4 The number of spots on the surface of an apple can be described by a Poisson Model with u = 1.6. Calculate the following: a) P(X= 1) (20 Marks b) P(2<x<3) (20 Marks) c) P(1 <X<4) (30 Marks) d) P(X>3) (30 Marks) END OF PAPER