Suppose a sample of 49 paired differences that have beenrandomly selected from a normally distributed population of paireddifferences yields a sample mean of d??=5.0d¯=5.0 and a samplestandard deviation of sd = 7.8.
(a) Calculate a 95 percent confidence intervalfor µd = µ1 –µ2. Can we be 95 percent confident that thedifference between µ1 andµ2 is greater than 0? (Round youranswers to 2 decimal places.)
Confidence interval = [ , ] ; (Click toselect)NoYes
(b) Test the null hypothesisH0: µd = 0 versus thealternative hypothesis Ha:µd ? 0 by setting ? equal to .10, .05, .01, and.001. How much evidence is there that µddiffers from 0? What does this say about how µ1and µ2 compare? (Round your answer to 3decimal places.)
| t = |
| Reject H0 at ? equal to (Click toselect)0.10.05no test values0.1,and 0.001all testvalues (Click to select)strongvery strongnosomeextremelystrong evidence that µ1 differs fromµ2. |
(c) The p-value for testingH0: µd < 3 versusHa: µd > 3 equals .0395.Use the p-value to test these hypotheses with ? equal to.10, .05, .01, and .001. How much evidence is there thatµd exceeds 3? What does this say about the sizeof the difference between µ1 andµ2? (Round your answer to 3 decimalplaces.)
| t = ; p-value |
| Reject H0 at ? equal to (Click to select)0.10and 0.050.05 and 0.010.05no test values.10 .05 .01 and .001, (Clickto select)extremely strongStrongNosomeVery strong evidence thatµ1 and µ2 differ by morethan 3. |
