Question

Exercise 10.16 METHODS AND APPLICATIONS 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 = 5.9 and a sample standard deviation of sd = 6.9. (a) Calculate a 95 percent confidence interval for Hd = 41 - 42. Can we be 95 percent confident that the difference between H1 and P2 is greater than 0? (Round your answers to 2 decimal places.) Confidence interval = [ ]; (Click to select) (b) Test the null hypothesis Ho: Md = 0 versus the alternative hypothesis Hai Hd70 by setting a equal to 10, .05, 01, and .001. How much evidence is there that he differs from 0? What does this say about how 1 and H2 compare? (Round your answer to 3 decimal places.) Reject Ho at a equal to (Click to select) differs from H2 (Click to select) evidence that Hi. (c) The p-value for testing Ho: Hd <3 versus Hai Hd > 3 equals .0025. Use the p-value to test these hypotheses with a equal to 10, .05, .01, and .001. How much evidence is there that ur exceeds 3? What does this say about the size of the difference between H1 and u2? (Round your answer to 3 decimal places.) ta ; p-value Reject Ho at a equal to .10.05.01 and .001 differ by more than 3. Very strong evidence that M1 and 2

Answer 1

a)

sample mean 'x̄=	5.900
sample size   n=	49.00
sample std deviation s=	6.900
std error 'sx=s/√n=	0.9857

for 95% CI; and 48 df, value of t=		2.011
margin of error E=t*std error    =		1.982
lower bound=sample mean-E =		3.918
Upper bound=sample mean+E =		7.882
from above 95% confidence interval for population mean =(3.92,7.88) ; reject Ho

b)

test stat t ='(x-μ)*√n/sx=

5.986

reject Ho at all value of alpha , extremly strong evidence

c)

test stat t ='(x-μ)*√n/sx=

2.942

p value      =

0.003