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46. A particular psychological test is used to measure student's resilience during the COVID-19 pandemic. The average test score for all university students nationwide is 115. A university in the south of the country estimates the mean test score for students in its economic faculty by testing a random sample of n students and constructing a confidence interval based on their scores. Which of the following statements about the confidence interval are true? i. The resulting interval will contain 115 ii. The 95 percent confidence interval based on " - 100 observations will generally be more narrow than the 95 percent confidence interval based on n - 50 observations. ini. When " -100. the 95 percent confidence interval will be wider than the 90 percent confidence interval. (a) ii only. (b) ii and ini (c) i only. (d) iii only. 47. For two events A and B in a sample space, the following probabilities are given: P(A UB) - 0.8, P(B) - 0.30 and P(A B) - 0.6. The numerical value of P(A) is: (a) 0.68. (b) 0.38. (c) 0.12. (d) Not enough inforination given to determine P (4). 48. Two researchers, Lesedi and Uphile, each select random samples of size 1000 from different populations and construct 95% confidence intervals for the proportion of those populations. The half-width of Lesedi's interval is 0.030 and the half-width of Uphile's is 0.025. Given that the sample proportions were 0.20 and 0.40, match cuch researcher with her sample proportion. (a) Lesedi's proportion is twice Uphile's proportion, (b) Lesedi's proportion is 0.40 and Uphile's proportion is 0.20. (c) Not sufficient information to answer the question. (d) Lesedi's proportion is 0.20 and Uphile's proportion is 9,40