Question

Suppose a sample of 49 paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean of d⎯⎯=5.0d¯=5.0 and a sample standard deviation of s_d = 7.8.

(a) Calculate a 95 percent confidence interval for µ_d = µ₁ – µ₂. Can we be 95 percent confident that the difference between µ₁ and µ₂ is greater than 0? (Round your answers to 2 decimal places.)

Confidence interval = [ ,  ] ; (Click to select)NoYes

(b) Test the null hypothesis H₀: µ_d = 0 versus the alternative hypothesis H_a: µ_d ≠ 0 by setting α equal to .10, .05, .01, and .001. How much evidence is there that µ_d differs from 0? What does this say about how µ₁ and µ₂ compare? (Round your answer to 3 decimal places.)

t =

Reject H0 at α equal to (Click to select)0.10.05no test values0.1,and 0.001all test values  (Click to select)strongvery strongnosomeextremely strong evidence that µ1 differs from µ2.

(c) The p-value for testing H₀: µ_d < 3 versus H_a: µ_d > 3 equals .0395. Use the p-value to test these hypotheses with α equal to .10, .05, .01, and .001. How much evidence is there that µ_d exceeds 3? What does this say about the size of the difference between µ₁ and µ₂? (Round your answer to 3 decimal places.)

t =  ; p-value

Reject H0 at α equal to (Click to select)0.10 and 0.050.05 and 0.010.05no test values.10 .05 .01 and .001, (Click to select)extremely strongStrongNosomeVery strong evidence that µ1 and µ2 differ by more than 3.

Answer 1

a) At 95% confidence interval the critical value is t^* = 2.011

The 95% confidence interval is

+/- t^* * s_d/

= 5 +/- 2.011 * 7.8/

= 5 +/- 2.24

= 2.76, 7.24

b) The test statistic t = ()/(s_d/)

                                 = (5 - 0)/(7.8/)

                                 = 4.487

P-value = 2 * P(T > 4.487)

            = 2 * (1 - P(T < 4.487))

            = 2 * (1 - 1) = 0

Reject H₀ at alpha equal to all test values. There is extremely strong evidence that differs from .

c) Reject H₀ at alpha equal to 0.10 and 0.05. There is very strong evidence that and differ by more than 3.