Suppose a sample of 49 paired differences that have beenrandomly selected from a normally distributed population of paireddifferences yields a sample mean d?? =4.1d¯ =4.1 of and a samplestandard deviation of sd = 6.8.

(a) Calculate a 95 percent confidence intervalfor µd = µ1 – µ2. Can we be 95 percent confident that thedifference between µ1 and µ2 is greater than 0? (Round youranswers to 2 decimal places.)

Confidence interval = [ ,  ] ; (Click toselect)YesNo

(b) Test the null hypothesis H0: µd = 0 versusthe alternative hypothesis Ha: µd ? 0 by setting ? equal to .10,.05, .01, and .001. How much evidence is there that µd differs from0? What does this say about how µ1 and µ2 compare? (Roundyour answer to 3 decimal places.)

t=

RejectH0 at ? equal to (Click to select)all testvaluesno test values0.10.1,and 0.0010.05  (Click toselect)nosomestrongvery strongextremely strong evidence thatµ1 differs from µ2.

(c) The p-value for testing H0: µd < 3versus Ha: µd > 3 equals .1316. Use the p-value to test thesehypotheses with ? equal to .10, .05, .01, and .001. How muchevidence is there that µd exceeds 3? What does this say about thesize of the difference between µ1 and µ2? (Round youranswer to 3 decimal places.)

t=  ; p-value

RejectH0 at ? equal to (Click to select)notest values0.050.10 and 0.05.10 .05 .01 and .0010.05 and 0.01,(Click to select)Very strongextremely strongsomeStrongNo evidencethat µ1 and µ2 differ bymore than 3.

rev: 07_14_2017_QC_CS-93578, 12_08_2018_QC_CS-150993