RI S5 Hypothesis Testing_Tutorial Qns

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 __________________________ Tutorial S5: Hypothesis Testing Page 1 of 4 Tutorial S5: Hypothesis Testing 1 Observations over a long period of time have shown that the mid-day temperature at a particular place during the month of June has a mean value of 23.9C. An ecologist sets up an experiment to collect data for a hypothesis test of whether the climate is getting hotter. She selects at random 20 June days over a five-year period and records the mid-day temperature. Her results (in C) are as follows : 20.1 26.2 23.3 28.9 30.4 28.4 17.3 22.7 25.1 24.2 15.4 26.3 19.3 24.0 19.9 30.3 32.1 26.7 27.6 23.1 (i) State the null and alternative hypotheses that the ecologist should use. (ii) Given that the standard deviation is 2.3C, carry out an appropriate test at the 10% significance level, stating any assumptions made. State your conclusion with regard to the mid-day temperature. [(ii) p-value = 0.0980 ≤ 0.1, reject H0] 2 ‘Brilliant’ fireworks are intended to burn for 40 seconds. A random sample of 50 ‘Brilliant’ fireworks is taken. Each firework in the sample is ignited and the burning time, x seconds, is measured. The results are summarised by ( 40) 27x  , 2( 40) 167x  . Test, at the 5% level of significance, whether the mean burning time of ‘Brilliant’ fireworks differs from 40 seconds. [7] State what you understand by the expression ‘at the 5% significance level’ in the context of this question. [1] State with a reason, whether, in using the above test, it is necessary to assume that the burning times of ‘Brilliant’ fireworks have a normal distribution. [1] [ p-value = 0.0304 ≤ 0.05, reject H0] 3 The mass, xkg, of the contents of each packet in a random sample of 80 cereal packets is measured, and the results are summarized by 79.53x , 2 100.4621x  . Test, at the 4% significance level, whether the population mean mass of the contents is less than 1.10 kg. [7] In another test, using the same data and also at the 4% significance level, the hypotheses are as follows. Null hypothesis: the population mean mass of the contents is equal to 0 kg Alternative hypothesis: the population mean mass of the contents is not equal to 0 kg Given that the null hypothesis is rejected in favour of the alternative hypothesis, find the set of possible values of 0 . [3] [ p-value0.0344 0.04  , reject 0H ; 0, 0.875 1.11,  ]

Raffles Institution H2 Mathematics 2025 Year 6 _________________________________________________________________________________________________ __________________________ Tutorial S5: Hypothesis Testing Page 2 of 4 4 An office worker, Natalie, has diabetes and has to monitor her blood glucose levels, which vary throughout the day. The results from a sample of 75 readings, x (in mmol/L), taken at random times over a week, are summarised by 511.5x and 2 4