Test the claim below about the mean of the differences for a population of paired data at the level of significance $α$ . Assume the samples are random and dependent, and the populations are normally distributed.
Claim: $μ_{d} = 0; α = 0.01$ . Sample statistics: $\bar{d} = 2.9, s_{d} = 8.63, n = 9$

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Answer

$Reject H_{0} if | t | > t_{α / 2, n - 1} = t_{0.005, 8}$

Steps

Step 1 ： $H_{0} : μ_{d} = 0, H_{1} : μ_{d} \neq 0$

Step 2 ： $t = \frac{\bar{d} - μ_{d}}{s_{d} / \sqrt{n}} = \frac{2.9 - 0}{8.63 / \sqrt{9}} \approx 1.0065$

Step 3 ： $Reject H_{0} if | t | > t_{α / 2, n - 1} = t_{0.005, 8}$