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# To test $H_{0}: \mu=80$ versus $H_{1}: \mu<80$, a simple random sample of size n=22 is obtained from a population that is known to be normally distributed.If $\bar{x}=76.9$ and s=8.5, compute the test statistic.

Solution

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Given:

$H_0:\mu=80$

$H_1:\mu<80$

$n=22$

$\overline{x}=76.9$

$s=8.5$

$\alpha=0.02$

Determine the value of the test statistic:

$t=\dfrac{\overline{x}-\mu_0}{s/\sqrt{n}}=\dfrac{76.9-80}{8.5/\sqrt{22}}\approx -1.711$

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