T2+W9+Hypothesis+Testing+%28Qn%29

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 _______________________________ Y6 H2 Math Term 2 Revision W9 Hypothesis Testing Page 1 of 1 Term 2 W9 Revision`: Hypothesis Testing Questions 1 DHS JC2 Mid-Year CT 9758/2018/02/Q1 The government of a particular country reported that the mean monthly water consumption of households is 317.9 m . This is followed by a nationwide water conservation campaign to encourage households to reduce their water consumption. Subsequently after the campaign, the water consumption 3 mx of a random sample of 50 households is recorded and their data are summarised as follows. ( 15) 103,x  2( 15) 599.x  (i) Find unbiased estimates of the population mean and variance. [2] (ii) Test at the 5% significance level whether the campaign is effective. State, giving a reason, whether any assumption about the distribution of the monthly water consumption of households is needed in order for the test to be valid. [4] (iii) Explain the meaning of ‘5% significance level’ in the context of the question. [1] 2 RI Prelim 9758/2020/02/Q7 In a factory, machines pack sugar into bags of 1 kg each on average, with variance 2 kg2. The manufacturer is concerned that the machines are putting too much sugar into the bags and decides to carry out a hypothesis test. A random sample of 8 bags are selected and their total mass is 8.4 kg. (i) Stating a necessary assumption, carry out a test of the manufacturer’s concern at the 5% significance level if 0.08 . [5] (ii) Use an algebraic method to calculate the range of values of 2 for which the null hypothesis would not be rejected at the 5% significance level. [3] 3 ACJC Prelim 9758/2019/02/Q7 modified A concert promoter claims that the mean price of a ticket to a pop concert is $200. A media company took a large random sample of n tickets, and found that the average ticket price for the sample is $206. If the standard deviation of ticket price is known to be $32.25, find the minimum value of n such that there is sufficient evidence at the 4% level of significance to reject the concert promoter’s claim. [4]