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# (Solved): A sample of size 21 , taken from a population whose standard deviation is unknown, has a sample mea ...

A sample of size 21 , taken from a population whose standard deviation is unknown, has a sample mean of $$74.96$$ and a sample standard deviation of $$8.80$$. Suppose that we have adopted the null hypothesis that the actual population mean is equal to 71 , that is, $$H_{0}$$ is that $$\mu=71$$ and we want to test the alternative hypothesis, $$H_{1}$$, that $$\mu \neq 71$$, with level of significance $$\alpha=0.01$$. a) What type of test would be appropriate in this situation? A right-tailed test. A left-tailed test. A two-tailed test None of the above. b) What is the computed $$p$$-value? For full marks your answer should be accurate to at least three decimal places. This will require a statistical calculator or software package. c) Based on your $$p$$-value and the decision rule you have decided upon, what can we conclude about $$H_{0}$$ ? There is sufficient evidence, at the given significance level, to reject $$H_{0}$$. There is insufficient evidence, at the given significance level, to reject $$H_{0}$$; or we fail to reject $$H_{0}$$. There is insufficient evidence to make it clear as to whether we should reject or not reject the null hypothesis

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