A firm makes a certain type of battery－powered toy．The battery life is denoted by $$\(X\)$$ hours and the population mean of $$\(X\)$$ is supposed to be 12 ．The Quality Control department wished to test whether the population mean of $$\(X\)$$ is actually less than 12．They tested a random sample of 50 of these toys and found that the sample mean， $$\(\bar{X}\)$$ ，was 11．4． （c）It is given that the value $$\(\bar{X}=11.4\)$$ leads to rejection of the null hypothesis at the $$\(\alpha \%\)$$ significance level． Find the set of possible values of $$\(\alpha\)$$ ． ［2］ . . . . . . . .

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