C291MT2013_Solutions

# 4 minutes reason σn 225 04 ii 2 marks b 01056 reason

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0.4 minutes (Reason: σ/√n = 2/√25 = 0.4) (ii) [2 marks] B. 0.1056 (Reason: Pr( < 7.5) = Pr(Z < [7.5-8]/0.4) = Pr(Z < -1.25) = 0.1056 e) [4 marks] D. z-scores: 3, 2.25, 7.5, 10 Computations: z-score for A = [79-70]/3 = 3 z-score for B = [74-65]/4 = 2.25 z-score for C = [68-65]/[4/√100] = 7.5 z-score for D = [73-70]/[3/√100] = 10 D has the highest z-score and therefore is the most unlikely. Question 7 (12 marks) a) (i) [2 marks] B. 269 (Reason: n = (1.645 2 )(0.46)(0.54)/(0.05 2 ) = 269) (ii) [2 marks] C. Increase the sample size (iii) [2 marks] A. [ 40.1% , 47.2% ] (Reason:=229/525 = 0.4362; 90% CI: 0.4362 ± 1.645√[(0.4362)(0.5638)/525] = 0.4362 ± 0.0356 or [0.4006, 4718]) b) [6 marks] 1. False (Reason: interval changes from sample to sample) 2. False (Reason: Population parameters don’t vary; sample statistics vary) 3. True (Reason: Higher confidence requires wider intervals) 4. False (Reason: CIs are not about individual data values; they are about estimates) 5. False (Reason: All CIs for mean include the sample mean; only 95% include the population mean) 6. True (Reason: Definition of a CI) Question 8 (8 marks) A. Is significantly higher than 28% e) [1 mark] C. A 95% confidence interval for p would not contain 28%. f) [2 marks] B. 2000 (Reason: Sampling variability only depends on sample size, as long the population is large) 2

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Question 9 (10 marks) *** END OF EXAM *** 3
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