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In a certain population, it is claimed that the mean number of years of education is 12.3, while the standard deviation is 2.3 years. A random sample of 50 people is drawn from this population, and the sample mean is 12.94 years. If the level of significance is set to \( \alpha=0.05 \), what is the area of the rejection region, and where is it located?
1. Identify the hypotheses
The null and alternative hypotheses are as follows:
\( \mathrm{HO}: \mu= \) ?
ŠŠ°: \( \mu \neq \) ?
2. Identify the rejection region
The sample size \( n= \) ? is greater than ?, and the population standard deviation is known. Also, the alternative hypothesis uses the relation symbol \( \neq \). Thus, a two-tailed z-test should be used.