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# (Solved): fast pls  8. The class average of a math class last semester was $$\mu=6.55$$. We may assume ...

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8. The class average of a math class last semester was $$\mu=6.55$$. We may assume that $$x$$ has a normal distribution with a standard deviation $$\sigma=0.4$$. A random sample of size 9 had a mean of $$\bar{x}=6.63$$. Use a $$\alpha=0.05$$ level of significance to test whether the class average $$\mu$$ is less than $$6.55$$ by doing the following: a) State the null hypothesis $$H_{0}$$ and the alternate hypothesis $$H_{1}$$. b) What is the value of the test statistic? c) Find the P-value of the test statistic. d) Based on your answers for parts $$(a)$$ through $$(c)$$, will you reject or fail to reject the null hypothesis? Explain your answer. a) State the null hypothesis $$H_{0}$$ and the alternate hypothesis $$H_{1}$$. Null hypothesis $H_{0}:$ Alternative hypothesis $$\quad H_{1}$$ : b) What is the value of the test statistic? $\mu=\quad \sigma=\quad \bar{x}=\quad n=$ test statistic $$z=\frac{\sqrt{n}(\bar{x}-\mu)}{\sigma}=$$ test statistic $$z=$$ c) Find the P-value of the test statistic $$z$$. $\boldsymbol{z}=$ d) Based on your answers for parts $$(a)$$ through $$(c)$$, will you reject or fail to reject the null hypothesis? Explain your answer. $$\mathrm{P}-$$ value $$=$$ Level of significance $$\alpha=$$ Interpretation:

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