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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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