A firm makes a certain type of battery－powered toy．The battery life is denoted by $$$X$$$ hours and the population mean of $$$X$$$ is supposed to be 12 ．The Quality Control department wished to test whether the population mean of $$$X$$$ is actually less than 12．They tested a random sample of 50 of these toys and found that the sample mean， $$$\bar{X}$$$ ，was 11．4．（a）State suitable null and alternative hypotheses for the test．［1］ . . . You may assume that the standard deviation of the battery life is 2.3 hours．

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s25_qp_65 Year：2025 Question No：7(a)

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Knowledge points:

6.5.1 understand the nature of a hypothesis test, the difference between one-tailed and two-tailed tests, and the terms null hypothesis, alternative hypothesis, significance level, rejection region (or critical region), acceptance region and test statistic (Outcomes of hypothesis tests are expected to be interpreted in terms of the contexts in which questions are set.)

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