[Solution Library] A paired difference experiment produced the following results: n_d=38 x̄_1=92 x̄_2=95.5 d#772;=-3.5 s_d^2=21 Determine the values of


Question: A paired difference experiment produced the following results:

\[n_{\mathrm{d}}=38 \quad \bar{x}_{1}=92 \quad \bar{x}_{2}=95.5 \quad \overline{\mathrm{d}}=-3.5 \quad s_{\mathrm{d}}^{2}=21\]
  1. Determine the values of \(z\) for which the null hypothesis, \(\mu_{1}-\mu_{2}=0\), would be rejected in favor of the alternative hypothesis, \(\mu_{1}-\mu_{2}<0 .\) Use \(\alpha=.10\)
  2. Conduct the paired difference test described in part a. Draw the appropriate conclusions.
  3. What assumptions are necessary so that the paired difference test will be valid?
  4. Find a \(90 \%\) confidence interval for the mean difference \(\mu_{\mathrm{D}}\)
  5. Which of the two inferential procedures, the confidence interval of part d or the test of hypothesis of part b, provides more information about the differences between the population means?

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