Question Number 1 [10 Marks In a random experiment each success and failure has a certain probability of occurrence. This probability can be used to find overall probability of the required outcome. Consider a similar scenario in which a machine shop orders 500 bolts from a supplier. To determine whether to accept the shipment of bolts, the manager of the facility randomly selected 12 bolts. If none of the 12 randomly selected bolts is found to be defective, he can conclude that the shipment is acceptable a) If 10% of the bolts in the population are defective, what is the probability that none of the selected bolts are defective? 151 b) How do you think can a prediction be made about getting non defective bolts if 10% of the bolts in the population are defective? Discuss your conclusions. 151 Marks Distribution/ Rubrics (for each part): Clarity/legibility -1 Mark Correct Approach = 1 Mark Full Steps - 1 Mark Develop possible answer - 2 Marks Question Number 2 [12 Marks An investor wants to know if the average value of property is greater than PKR 75000/=. She made a sample by collecting data of different monetary values of that property from different estate agents. Accordingly, the provided property values in Pakistan Rupee (PKR) are, PKR 71,000/-, PKR 83,000/-, PKR 90,000, PKR 77,000/-, PKR 68000/- and PKR 72000/= Sample mean is PKR 77,500/= and standard deviation of this sample is PKR 9,050/- a) Estimate the population mean interval at 90% CI, 121 b) Can the investor have 90 percent confidence (90% CI) that the mean value for the property would be different from PKR 75000/-? Perform the required hypothesis test and support your answer from part (a). 121 c) Assuming that distribution of alternate hypothesis is centralized at PKR 85,000, using same standard error of mean as for null hypothesis graph the null, alternate hypotheses distributions by shading Type 1 and Type 2 error regions on them, sensitivity and power (specificity) of the test taking a=0.1. 121 d) Assuming that distribution of alternate hypothesis is centralized at PKR 65,000, using same standard error of mean as for null hypothesis graph the null, alternate hypotheses distributions by shading Type 1 and Type 2 error regions on them, sensitivity and power (specificity) of the test taking a=0.1 and B-20% 121 e) How Type 1 and Type 2 errors effect each other in context to this question? 12] f) What is your understanding for statistical significance in context to this question? Illustrate your answer in the light of probability value we get for FP rate, FN rate, sensitivity and power of the test (specificity) 121 Page 2 of 3 Marks Distribution/ Rubrics (for each part): Clarity/legibility -0.5 Mark Correct Approach -0.5 Mark Full Steps -0.5 Mark Develop possible answer -0.5 Mark
