To test (H_{0}: mu=20) versus (H_{1}: mu <20), a simple random sample of size (n=18) is obtained

Question:

To test $H_{0}: \mu=20$ versus $H_{1}: \mu<20$, a simple random sample of size $n=18$ is obtained from a population that is known to be normally distributed.

(a) If $\bar{x}=18.3$ and $s=4.3$, compute the test statistic.

(b) Draw a $t$-distribution with the area that represents the $P$-value shaded.

(c) Approximate and interpret the $P$-value.

(d) If the researcher decides to test this hypothesis at the $\alpha=0.05$ level of significance, will the researcher reject the null hypothesis? Why?

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