Questions: Assume that the differences are normally distributed. Complete parts (a) through (d). Observation 1 2 3 4 5 6 7 8 Xi 44.9 48.1 45.3 39.7 46.4 53.8 45.5 43.3 Yi 45.1 48.5 47.8 45.1 48.2 53.9 48.4 45.5 sd=1.775 (Round to three decimal places as needed.) (c) Test if μd<0 at the α=0.05 level of significance. What are the correct null and alternative hypotheses? A. H0: μd=0 B. H0: μd>0 H1: μd<0 H1: μd<0 C. H0: μd<0 D. H0: μd<0 H1: μd>0 H1: μd=0 Find the test statistic for this hypothesis test. t0=-3.09 (Round to two decimal places as needed.) Determine the P -value for this hypothesis test. P -value = 0.010 (Round to three decimal places as needed.) Choose the correct conclusion. A. Do not reject the null hypothesis. There is sufficient evidence that μd<0 at the α=0.05 level of significance. B. Reject the null hypothesis. There is sufficient evidence that μd<0 at the α=0.05 level of significance. C. Do not reject the null hypothesis. There is insufficient evidence that μd<0 at the α=0.05 level of significance. D. Reject the null hypothesis. There is insufficient evidence that μd<0 at the α=0.05 level of significance. (d) Compute a 95% confidence interval about the population mean difference μd. The lower bound is The upper bound is (Round to two decimal places as needed.)

Transcript text: Assume that the differences are normally distributed. Complete parts (a) through (d). \begin{tabular}{lcccccccc} Observation & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ $X_{i}$ & 44.9 & 48.1 & 45.3 & 39.7 & 46.4 & 53.8 & 45.5 & 43.3 \\ $Y_{i}$ & 45.1 & 48.5 & 47.8 & 45.1 & 48.2 & 53.9 & 48.4 & 45.5 \end{tabular} $s_{d}=1.775$ (Round to three decimal places as needed.) (c) Test if $\mu_{d}<0$ at the $\alpha=0.05$ level of significance. What are the correct null and alternative hypotheses? A. $H_{0}: \mu_{d}=0$ B. $H_{0}: \mu_{d}>0$ $H_{1}: \mu_{d}<0$ $H_{1}: \mu_{d}<0$ C. $H_{0}: \mu_{d}<0$ D. $H_{0}: \mu_{d}<0$ \[ H_{1}: \mu_{d}>0 \] \[ \mathrm{H}_{1}: \mu_{\mathrm{d}}=0 \] Find the test statistic for this hypothesis test. \[ t_{0}=-3.09 \text { (Round to two decimal places as needed.) } \] Determine the P -value for this hypothesis test. P -value $=$ $\square$ 0.010 (Round to three decimal places as needed.) Choose the correct conclusion. A. Do not reject the null hypothesis. There is sufficient evidence that $\mu_{\mathrm{d}}<0$ at the $\alpha=0.05$ level of significance. B. Reject the null hypothesis. There is sufficient evidence that $\mu_{\mathrm{d}}<0$ at the $\alpha=0.05$ level of significance. C. Do not reject the null hypothesis. There is insufficient evidence that $\mu_{\mathrm{d}}<0$ at the $\alpha=0.05$ level of significance. D. Reject the null hypothesis. There is insufficient evidence that $\mu_{\mathrm{d}}<0$ at the $\alpha=0.05$ level of significance. (d) Compute a $95 \%$ confidence interval about the population mean difference $\mu_{\mathrm{d}}$. The lower bound is $\square$ The upper bound is $\square$ (Round to two decimal places as needed.)