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 ¯ =5.3 d¯=5.3 and a sample standard deviation of sd = 7.2.

(a) Calculate a 95 percent confidence interval for µd = 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 = [ , ] ;

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)0.05no test values0.10.1,and 0.001all test values (Click to select)extremely strongnosomestrongvery strong evidence that µ1 differs from µ2.

(c) The p-value for testing H₀: µ_d < 3 versus H_a: µ_d > 3 equals .0150. 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).10 .05 .01 and .0010.05 and 0.010.05no test values0.10 and 0.05, (Click to select)extremely strongNosomeVery strongStrong evidence that µ1 and µ2 differ by more than 3.

Answer 1

(a)

Interpretation:

Since confidence does not contain zero and all values are positive so we can conclude that there is evidence that µ_d differs from 0.

Since all values are positive so we can be 95 percent confident that the difference between µ1 and µ2 is greater than 0.

(b)

The test statistics is t = 5.153

The p-value is: 0.000

Conclusion :

Reject H₀ at α equal to all test values Extreme strong evidence that µ₁ differs from µ₂.

(c)

The test statistics is t = 2.236

The p-value is: 0.015

Reject H₀ at α equal to .10 and .05 Strong evidence that µ₁ and µ₂ differ by more than 3.