Question

Chapter 6, Section 5, Exercise 238 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 Ho : μι-μ. vs Ha : Hj < u2 using the paired data in the following table: Treatment14 12 5215 14 22 Treatment 2 18 19 252 19 14 15 20

Answer 1

null Hypothesis:4 <= alternate Hypothesis: H4 for 0.05 level with left tailed test andn-1= 7 df, critical value of t= Decision rule: reject Ho if test statistic K-1.895 1.895 S. No diff:(d)=x1-x2 treatment 1 treatment 2 14 18 -4 16.00 2 12 19 -7 49.00 15 25 -10 100.00 4 21 21 0.00 15 19 -4 16.00 11 14 -3 9.00 14 15 -1 1.00 22 20 2 4.00 total Id=-27 zd2=195 -3.3750 mean dbar= degree of freedom =n-1 7.000 Std deviaiton S,=v(zd²-(zd)?In}l(n-1) = std error=Se=SpAn= 3.852 1.3620 (d-ud)/Se -2.48 test statistic p value 0.021

from above

test statistic t =-2.48

p value =0.021