Question

Chapter 6, Section 5, Exercise 236 Use a t-distribution and the given matched pair sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distribution of the differences is relatively normal. Assume that differences are computed using d = x1-x2. Test H0 : ud=0 vs H0 : ud /= 0 using the paired difference sample results x bar = 14.46, S= 13.0, n=25

Give the test statistic and the p-value. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.

test statistic = Enter your answer;

test statistic p-value = Enter your answer;

p-value Give the conclusion using a 5% significance level.

Reject or Do not reject .

Answer 1

Ho :µd=0

Ha :µd ╪0

Level of Significance , α = 0.05

sample size , n = 25

mean of difference , D̅ =14.46

std dev of difference , Sd = 13.0

std error , SE = Sd / √n = 2.60

t-statistic   = (D̅ - µd)/SE   = 5.56

Degree of freedom,    DF=n - 1 = 24

p-value = 0.000

Conclusion:                            p-value <α=0.05 , Reject null hypothesis