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⎯⎯=4.2d¯=4.2 and a sample standard deviation of s_d = 7.6.

(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)YesNo

(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)all test valuesno test values0.1,and 0.0010.050.1  (Click to select)very strongextremely strongnostrongsome evidence that µ1 differs from µ2.

(c) The p-value for testing H₀: µ_d < 3 versus H_a: µ_d > 3 equals .1373. Use the p-value to test these hypotheses with α equal to .10, .05, .01, and .001. How much evidence is there that µ_dexceeds 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)no test values0.050.05 and 0.010.10 and 0.05.10 .05 .01 and .001, (Click to select)someVery strongStrongNoextremely strong evidence that µ1 and µ2 differ by more than 3.

Answer 1

(a) Hypothesis : VS

The 95 percent confidence interval for µ_d = µ₁ – µ_{2 is ,}

Here , does not lies in the 95% confidence interval

Therefore , The 95 percent confident that the difference between µ₁ and µ₂ is greater than 0

(b)  Hypothesis : VS

The test statistic is ,

P-value = ; From excel "=TDIST(3.87,48,2)"

Decision : Here , P-value <

Where , = 0.10 , 0.05 , 0.01 , 0.001

Therefore , reject Ho

Conclusion : Hence , there is sufficient evidence to conclude that the differs from

(c) Since , P-value = 0.1373

Decision : Here , P-value >

Where , = 0.10 , 0.05 , 0.01 , 0.001

Therefore , fail to reject Ho

Conclusion : Hence , there is not sufficient evidence to conclude that the and differs by more than 3.