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Research commissioned by Vodafone suggests that older workers are the happiest employees (BBC News, July 21, $2008$). The report documents that $70 \%$ of older workers in England feel fulfilled, compared with just $50 \%$ of younger workers. A demographer believes that an identical pattern does not exist in Asia. A survey of $120$ older workers in Asia finds that $75$ feel fulfilled. A similar survey finds that $58 \%$ of 210 younger workers feel fulfilled.

b. At the $5 \%$ level of significance, test if younger workers in Asia feel more fulfilled than their British counterparts.

Solution

VerifiedThe goal of this task is to construct null and alternative hypotheses to test whether younger workers in Asia feel more fulfilled than their own British colleagues, if we know that $50 \%$ young workers in England feel fulfilled.

A study conducted on a sample of $n = 210$ younger workers in Asia shows that $58 \%$ them feel fulfilled, which means that the sample proportion $\overline {p} = 0.58$.

It is necessary to test the claim at the level of significance of $5 \%$.

**Which steps do we need to follow to construct hypotheses?**

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