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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:

a) The null hypothesis for given problem is class average is less than ?is less than 6.55. H0 : ?<6.55 The alternative hypothesis for the given proble