2023 S7 Hypo Test BMQ APQ (RVHS)

2023 JC2 H2 Mathematics (9758) River Valley High School Mathematics Department Page 1 of 39 STATISTICS 7 TUTORIAL (SOLUTIONS) Hypothesis Testing H2 Maths Topic: Hypothesis testing Purpose of LE: LE:  Relate the notion of null and alternative hypothesis to the statement “innocent until proven guilty” To enhance understanding of the concept of null and alternative hypothesis and the asymmetry of these hypotheses by relating it to a concrete analogy which is easier to appreciate. Remarks:  Teachers can pose the question during lecture or tutorial to bring out the above idea, by asking students to compare the null and alternative hypothesis against the Singapore legal system “innocent until proven guilty”.  Amount of time required: 5 – 10 minutes Details of Activity Present the reading to the students. In pairs, discuss the concept of null and alternative hypothesis that you have just learned with the idea of “innocent until proven guilty” used in the Singapore legal system. The Singapore Legal System In Singapore, “The presumption of innocence is widely recognised as the cornerstone of the criminal justice system. Under the presumption, the Prosecution has a “duty” to prove the accused’s guilt, “subject to” the insanity defence and statutory exceptions. Hence, if there remains a “reasonable doubt … on the whole of the case”, the prosecution has not established its case and the accused is acquitted.” (http://www.eastasiareview.org/issues/2013/articles/2013_Low.pdf) (Available as of 11 Jul 2016) Notes for teachers The hypothesis test works like a criminal trial: defendants are presumed innocent until proven guilty. Imagine the following scenario: A suspect was put on trial for a criminal offence. The Prosecution thought that he was guilty. H0: Suspect was innocent H1: Suspect was guilty The Prosecution would try to show the judge, beyond reasonable doubt, that the suspect was guilty (in other words, there was enough evidence to “reject the null hypothesis”). If the Prosecution did not do his job well, then he would not have enough evidence to convict the suspect. Although the judge might still think that the suspect was guilty, but the judge could not legally prove it. In this case, with the given evidence, the jury would “fail to reject the null hypothesis”.

2023 JC2 H2 Mathematics (9758) River Valley High School Mathematics Department Page 2 of 39 Basic Mastery Question 1. The solution to the following problem is provided below the question. Highlight the errors in the solution and amend these errors. A manufacturer claims that the life span of an electrical component it produces is normally distributed with mean 22 hours and standard deviation 6 hours. A random sample of 50 such electrical components has a mean life span of 20