Question 3a The results of the 42.195km full marathon for the trials and actual run of the latest inter- university competition are summarised in Table Q3(a) below. Final Run More than 4.5 Under 4 hours 4 - 4.5 hours hours Under 4 58 50 46 hours Trial Run 4 - 4.5 hours 62 115 130 More than 4.5 hours 19 40 80 Table Q3(a) We are interested to determine if the performance in one run is associated with the performance in the other run.ENG 1237 PM Question 3a(i) Name an appropriate test procedure for analysing the data. RCL ENG Question 3a(ii) (1 mark) 8 Apply the statistical test at the 5% level of significance. 1. ii. State the null and alternative hypotheses. Compute the test statistic. iii. iv. Compare the test statistic against either critical region or P-value. *10 Draw conclusions in the context of the question. (16 marks) Question 3b The water bills for all 5 Room HDB households in Hougang have an unknown distribution with mean $160 and standard deviation $28. A survey of 120 households were conducted. Question 3b(i) Compute the probability that the mean water bill will be between $153 and $166. (3 marks) Question 3b(ii) What is the probability that the mean water bill will be within $6 of the population mean? (2 marks) Question 3b(iii) The Head Statistician wants to increase the sample size so that the width of the 95% confidence interval of the sample mean can be decreased to just $2. Compute the minimum (3 marks) sample size to meet this criteria. Page 7 of 9 MTH230 Copyright 2022 Singapore University of Social Sciences (SUSS) TOA - July Semester 2022