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 s_d = 7.8.

(a) Calculate a 95 percent confidence intervalfor µ_d = 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: µ_d = 0 versus thealternative hypothesis H_a:µ_d ? 0 by setting ? equal to .10, .05, .01, and.001. How much evidence is there that µ_ddiffers 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: µ_d < 3 versusH_a: µ_d > 3 equals .0395.Use the p-value to test these hypotheses with ? equal to.10, .05, .01, and .001. How much evidence is there thatµ_d 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.