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The data for a random samples of 8 paired observations art shown in the table 10 the right. - What are the approgriatu noif and atarnative hopotheses Io test whether the mean for populatice 2 in larger than that fer population 17 ? b. Conduat the that identifed in peit a using a a \( 0.10 \). c. Find a POXN conlidence interval for \( \mu \). Irderperet this revent. d. What asturnptions are necesnary to enere the valdity of this analynis? a. Wriat are the hypotheses for \( \mu_{4}=\left(\mu_{1}-\mu_{2}\right) \) ? A. He: Het 10 B. \( H_{2}: F_{2}>0 \) \( H_{g}-\mu_{d}=6 \) \( \mathrm{H}_{\mathrm{e}} \mathrm{Md}_{\mathrm{d}}=\mathrm{O} \) C. \( \mathrm{H}_{2}-\mathrm{Hg}_{2}=\mathrm{O} \) D. \( \mathrm{H}_{0}=\mathrm{He}_{\mathrm{a}}<\mathrm{O} \) F. Hir Hin \( =0 \) \( H_{e} \mu_{d}=0 \) \( H_{e}: R_{s}=0 \) b. Identify the rejection regian for testing the hypotheses from part a. Select the correct choice below and fin in the arswer box bo corrplote your choice. (Round to three decimal placos as needed.) A. \( 1 \times \) 8. 1? C. \|\|\( \geqslant \) Caloulate the test statistic.
\( \mathrm{t}= \) (Round to three decimal places as neoded.) Give the appropriate conclusion for the test. \( \mathrm{H}_{0} \) - Since the test statistic in the rejection region, there is evidence to conclude that the mean for population 2 is greater th c. The confide ince interval for \( \mu_{\mathrm{d}} \) is ( (RRound to two decimal places as neodod.) Interpret this fesult. Tha interyal 0 , which evidence that the mean for population 2 is greater than that for population 1. d. What conditions are required for the test results to be valid? Select all that apply. A. The variarices of the two populations are approximately the same. B. The populations being sampled are approximately normal.

Sol :-- (a) Null hypothesis :-- HO:?d=0 alternate hypothesis HO:?d<0 option (F) (b) by using given table N

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