RI S5 Hypothesis Testing_Add Prac_Qns

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 ______________________________________________________ Additional Practice Questions for Chapter S5: Hypothesis Testing Page 1 of 5 Additional Practice Questions for Chapter S5: Hypothesis Testing 1 The production manager of a food manufacturing company wishes to take a random sample of a certain type of biscuit bar from the thousands produced one day at his factory, for quality control purposes. He wishes to check that the mean mass of the bars is 32 grams, as stated on the packets. (i) State what it means for a sample to be random in this context. [1] The masses, x grams of a random sample of 40 biscuit bars are summarised as follows.     240 32 7.7 32 11.05n x x      (ii) Calculate unbiased estimates of the population mean and variance of the mass of biscuit bars. [2] (iii) Test at 1% level of significance, the claim that the mean mass of biscuit bars is 32 grams. You should state your hypotheses and define any symbols you use. [5] (iv) Explain why there is no need for the production manager to know anything about the population distribution of the masses of the biscuit bars. [2] 2 To investigate the length of time spent by students in the school canteen during lunch break, a random sample of 90 students was taken. The time, x minutes, spent by each student was measured and it was found that ( 40) 270x  and 2 167095x  . A previous survey indicated that students spent an average of 42.5 minutes in the canteen during lunch break. Test, at the 5% level, whether the average time spent has increased. [6] State what you understand by the expression ‘at the 5% significance level’ in the context of this question. [1] 3 A company produces resistors rated at 750 ohms for use in electronic circuits. The production manager wishes to test whether the mean resistance of these resistors is in fact 750 ohms. He knows that the resistances are normally distributed with variance 100 ohms2. (i) Explain whether the manager should carry out a 1-tail test or a 2-tail test. State hypotheses for the test, defining any symbols you use. [2] The production manager takes a random sample of 8 of these resistors. He finds that the resistances, in ohms, are as follows. 742 771 768 738 769 752 742 766 (ii) Find the mean of the sample of 8 resistors. Carry out the test, at the 5% level of significance, for the production manager. Give your conclusion in context. [5] The company also produces resistors rated at 1250 ohms. Nothing is known about the distribution of the resistances of these resistors. (iii) Describe how, and why, a test of the mean resistance of the 1250 ohms resistors would need to differ from that for the 750 ohms resistors. [2]

Raffles Institution H2 Mathematics 2025 Year 6 ______________________________________________________________________